Algebraic geometry Books
Cambridge University Press London Mathematical Society Student Texts 24 Lectures on Elliptic Curves 0024 London Mathematical Society Student Texts Series Number 24
Book SynopsisThe study of (special cases of) elliptic curves goes back to Diophantos and Fermat, and today it is still one of the liveliest centres of research in number theory. This book, which is addressed to beginning graduate students, introduces basic theory from a contemporary viewpoint but with an eye to the historical background. The central portion deals with curves over the rationals: the Mordell-Weil finite basis theorem, points of finite order (Nagell-Lutz) etc. The treatment is structured by the local-global standpoint and culminates in the description of the Tate-Shafarevich group as the obstruction to a Hasse principle. In an introductory section the Hasse principle for conics is discussed. The book closes with sections on the theory over finite fields (the 'Riemann hypothesis for function fields') and recently developed uses of elliptic curves for factoring large integers. Prerequisites are kept to a minimum; an acquaintance with the fundamentals of Galois theory is assumed, but no Trade Review'… an excellent introduction … written with humour.' Monatshefte für MathematikTable of ContentsIntroduction; 1. Curves of genus: introduction; 2. p-adic numbers; 3. The local-global principle for conics; 4. Geometry of numbers; 5. Local-global principle: conclusion of proof; 6. Cubic curves; 7. Non-singular cubics: the group law; 8. Elliptic curves: canonical form; 9. Degenerate laws; 10. Reduction; 11. The p-adic case; 12. Global torsion; 13. Finite basis theorem: strategy and comments; 14. A 2-isogeny; 15. The weak finite basis theorem; 16. Remedial mathematics: resultants; 17. Heights: finite basis theorem; 18. Local-global for genus principle; 19. Elements of Galois cohomology; 20. Construction of the jacobian; 21. Some abstract nonsense; 22. Principle homogeneous spaces and Galois cohomology; 23. The Tate-Shafarevich group; 24. The endomorphism ring; 25. Points over finite fields; 26. Factorizing using elliptic curves; Formulary; Further reading; Index.
£35.14
Cambridge University Press The Geometry of Total Curvature on Complete Open Surfaces 159 Cambridge Tracts in Mathematics Series Number 159
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£105.45
Cambridge University Press Algebraic Curves over Finite Fields Errorcorrecting Codes and Exponential Sums Cambridge Tracts in Mathematics Series Number 97
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£53.19
Cambridge University Press Singularities 201 London Mathematical Society Lecture Note Series Series Number 201
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£61.71
Cambridge University Press thealgebraiccharacterizationofgeometric4manifolds
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£55.09
Cambridge University Press Lectures on Arakelov Geometry 33 Cambridge Studies in Advanced Mathematics Series Number 33
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£47.49
Cambridge University Press Lectures on Vector Bundles 54 Cambridge Studies in Advanced Mathematics Series Number 54
Book SynopsisThis work consists of two courses on the moduli spaces of vector bundles. The first is introductory, and assumes very little background; the second is more advanced and takes the reader into current areas of research. This a treatment of vector bundles that will be welcomed by experienced algebraic geometers and novices alike.Trade Review'The whole book is well written and is a valuable addition to the literature … It is essential purchase for all libraries maintaining a collection in algebraic geometry, and strongly recommended for individual researchers and graduate students with an interest in vector bundles.' Peter Newstead, Bulletin of the London Mathematical SocietyTable of ContentsPart I. Vector Bundles On Algebraic Curves: 1. Generalities; 2. The Riemann-Roch formula; 3. Topological; 4. The Hilbert scheme; 5. Semi-stability; 6. Invariant geometry; 7. The construction of M(r,d); 8. Study of M(r,d); Part II. Moduli Spaces Of Semi-Stable Sheaves On The Projective Plane; 9. Introduction; 10. Operations on semi-stable sheaves; 11. Restriction to curves; 12. Bogomolov's theorem; 13. Bounded families; 14. The construction of the moduli space; 15. Differential study of the Shatz stratification; 16. The conditions for existence; 17. The irreducibility; 18. The Picard group; Bibliography.
£131.10
Cambridge University Press LMSST 34 Complex Algebraic Sur 2ed London Mathematical Society Student Texts Series Number 34
Book SynopsisDeveloped over more than a century, and still an active area of research today, the classification of algebraic surfaces is an intricate and fascinating branch of mathematics. In this book Professor Beauville gives a lucid and concise account of the subject, following the strategy of F. Enriques, but expressed simply in the language of modern topology and sheaf theory, so as to be accessible to any budding geometer. This volume is self contained and the exercises succeed both in giving the flavour of the extraordinary wealth of examples in the classical subject, and in equipping the reader with most of the techniques needed for research.Trade Review‘… a lucid and concise account of the subject.’ L’Enseignement MathématiqueTable of ContentsIntroduction; Notation; Part I. The Picard Group and the Riemann-Roch Theorem: Part II. Birational Maps: Part III. Ruled Surfaces: Part IV. Rational Surfaces: Part V. Castelnuovo’s Theorem and Applications: Part VI. Surfaces With pg = 0 and q > 1: Part VII. Kodaira Dimension: Part VIII. Surfaces With k = 0: Part IX. Surfaces With k = 1 and Elliptic Surfaces: Part X. Surfaces of General Type: Appendix A. Characteristic p; Appendix B. Complex surfaces; Appendix C. Further reading; References; Index.
£37.04
Cambridge University Press Abelian Functions
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£82.64
Cambridge University Press Computational Algebraic Geometry
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£34.19
Cambridge University Press Number Theory and Algebraic Geometry 303 London Mathematical Society Lecture Note Series Series Number 303
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£65.86
Cambridge University Press Current Topics in Complex Algebraic Geometry
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£105.45
Cambridge University Press Geometric Galois Actions Volume 2 the Inverse Galois Problem Moduli Spaces and Mapping Class Groups London Mathematical Society Lecture Note Series Series Number 243
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£84.07
Cambridge University Press Geometric Galois Actions Around Grothendiecks Esquisse DUn Programme London Mathematical Society Lecture Note Series Series Number 242
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£84.07
Cambridge University Press Birational Geometry of Algebraic Varieties 134 Cambridge Tracts in Mathematics Series Number 134
Book SynopsisOne of the major discoveries of the last two decades of the twentieth century in algebraic geometry is the realization that the theory of minimal models of surfaces can be generalized to higher dimensional varieties. This generalization, called the minimal model program or Mori's program, has developed into a powerful tool with applications to diverse questions in algebraic geometry and beyond. This book provides the a comprehensive introduction to the circle of ideas developed around the program, the prerequisites being only a basic knowledge of algebraic geometry. It will be of great interest to graduate students and researchers working in algebraic geometry and related fields.Trade ReviewReview of the hardback: '… the book is very crisply written, unusually easy to read for a book covering advanced material, and is moreover very concise for the book for reference, but is also an ideal book on which to base a series of seminars for research students, or indeed for research students to read by themselves.' P. M. H. Wilson, Bulletin of the London Mathematical SocietyReview of the hardback: '… a very good survey of present research.' European Mathematical SocietyReview of the hardback: 'I can recommend it to anyone wanting to get a deeper knowledge than just getting a survey of some facts on the classification theory.' M. Coppens, Niew Archief voor WiskundeReview of the hardback: '… a very good survey of present research … a very clear presentation of the subject.' EMSTable of Contents1. Rational curves and the canonical class; 2. Introduction to minimal model program; 3. Cone theorems; 4. Surface singularities; 5. Singularities of the minimal model program; 6. Three dimensional flops; 7. Semi-stable minimal models.
£95.00
Cambridge University Press Explicit Birational Geometry of 3folds 281 London Mathematical Society Lecture Note Series Series Number 281
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£71.65
Cambridge University Press Singularity Theory Proceedings of the European Singularities Conference August 1996 Liverpool and Dedicated to CTC Wall on the Occasion of his Lecture Note Series Series Number 263
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£61.71
Cambridge University Press Introduction to Algebraic Geometry
Book SynopsisFocuses on specific examples and develops only the formalism needed to address these. Introduces the notion of Gröbner bases early and develops algorithms for almost everything covered. Based on courses given over the past five years in a large interdisciplinary programme at Rice University, spanning mathematics, computer science, and bioinformatics.Trade Review'Yet another introduction to algebraic geometry? No! This is a book that has been missing from our textbook arsenal and that belongs on the bookshelf of anyone who plans to either teach or study algebraic geometry.' Sándor Kovács, University of Washington'The author accomplished his goals. He created a textbook that will serve as a bridge for many students and researchers to algebraic geometry.' Acta Scientiarum MathematicarumTable of ContentsIntroduction; 1. Guiding problems; 2. Division algorithm and Gröbner bases; 3. Affine varieties; 4. Elimination; 5. Resultants; 6. Irreducible varieties; 7. Nullstellensatz; 8. Primary decomposition; 9. Projective geometry; 10. Projective elimination theory; 11. Parametrizing linear subspaces; 12. Hilbert polynomials and Bezout; Appendix. Notions from abstract algebra; References; Index.
£37.99
Cambridge University Press Algebraic and Analytic Geometry 345 London Mathematical Society Lecture Note Series Series Number 345
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£87.39
Cambridge University Press Matroids
Book SynopsisMatroids provides a unified way to understand graph theory, linear algebra and combinatorics via finite geometry. This informal text provides a comprehensive introduction to matroid theory that emphasizes its connections to geometry and is suitable for undergraduates. It includes over 300 exercises, examples and projects suitable for independent study.Trade Review"The authors write in an entertaining, conversational style, and the text is often peppered with humorous footnotes. Nearly 300 exercises and scores of references will benefit motivated readers." -J. T. Saccoman, ChoiceTable of Contents1. A tour of matroids; 2. Cryptomorphisms; 3. New matroids from old; 4. Graphic matroids; 5. Finite geometry; 6. Representable matroids; 7. Other matroids; 8. Matroid minors; 9. The Tutte polynomial; Projects; Appendix: matroid axiom systems; Bibliography; Index.
£105.45
Cambridge University Press Current Developments in Algebraic Geometry
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£122.55
Cambridge University Press Hodge Theory and Complex Algebraic Geometry I Volume 1 76 Cambridge Studies in Advanced Mathematics Series Number 76
Book SynopsisThis is a completely self-contained modern introduction to Kaehlerian geometry and Hodge structure. The author proves the Kaehler identities, which leads to the hard Lefschetz theorem and the Hodge index theorem. Aimed at students, the text is complemented by exercises which provide useful results in complex algebraic geometry.Trade Review'This introductory text to Hodge theory and Kahlerian geometry is an excellent and modern introduction to the subject, shining with comprehensiveness, strictness, clarity, rigor, thematic steadfastness of purpose, and catching enthusiasm for this fascinating field of contemporary mathematical research. This book is exceedingly instructive, inspiring, challenging and user-friendly, which makes it truly outstanding and extremely valuable for students, teachers, and researchers in complex geometry.' Zentralblatt MATH'I would recommend anyone interested in learning about a topic in complex differential or algebraic geometry to read Voisin's volumes. She has done a remarkably good job.' Proceedings of the Edinburgh Mathematical Society'… this book is going to become a very common reference in this field … useful for both a student trying to learn the subject as well as the researcher that can find a wealth of results in a clear and compact format. The exposition is very precise and the introduction that precedes each chapter helps the reader to focus on the main ideas in the text.' Mathematical Reviews'The book provides a very satisfying exposition of all the methods of studying algebraic cycles that have come out of Hodge theory.' Bulletin of the London Mathematical Society'Mathematical rewards [await] those who invest their mathematical energies in this beautiful pair of volumes.' Bulletin of the AMSPrize Winner Cambridge University Press congratulates Claire Voisin, winner of the 2007 Ruth Lyttle Satter Prize in Mathematics!Table of ContentsIntroduction; Part I. Preliminaries: 1. Holomorphic functions of many variables; 2. Complex manifolds; 3. Kähler metrics; 4. Sheaves and cohomology; Part II. The Hodge Decomposition: 5. Harmonic forms and cohomology; 6. The case of Kähler manifolds; 7. Hodge structures and polarisations; 8. Holomorphic de Rham complexes and spectral sequences; Part III. Variations of Hodge Structure: 9. Families and deformations; 10. Variations of Hodge structure; Part IV. Cycles and Cycle Classes: 11. Hodge classes; 12. Deligne-Beilinson cohomology and the Abel-Jacobi map; Bibliography; Index.
£116.85
Cambridge University Press Hodge Theory and Complex Algebraic Geometry II Volume 2 77 Cambridge Studies in Advanced Mathematics Series Number 77
Book SynopsisThe 2003 second volume of this self-contained account of Kaehlerian geometry and Hodge theory continues Voisin's study of topology of families of algebraic varieties and the relationships between Hodge theory and algebraic cycles. Aimed at researchers, the text includes exercises providing useful results in complex algebraic geometry.Trade Review'All together, the author has maintained her masterly style also throughout this second, much more advanced volume, just as expected. The entire two-volume text is highly instructive, inspiring, reader-friendly and generally outstanding. Without any doubt, these two volumes must be seen as an indispensible standard text on transcendental algebraic geometry for advanced students, teachers, and also researchers in this contemporary field of mathematics. The author provides, simultaneously and in a unique manner, both a complete didactic exposition and an up-to-date presentation of the subject, which is still a rather exceptional feature in the textbook literature.' Zentralblatt MATH'The book provides a very satisfying exposition of all the methods of studying algebraic cycles that have come out of Hodge theory.' Bulletin of the London Mathematical Society'I would recommend anyone interested in learning about a topic in complex differential or algebraic geometry to read Voisin's volumes. She has done a remarkably good job.' Proceedings of the Edinburgh Mathematical Society'… this book is going to become a very common reference in this field … useful for both a student trying to learn the subject as well as the researcher that can find a wealth of results in a clear and compact format. The exposition is very precise and the introduction that precedes each chapter helps the reader to focus on the main ideas in the text.' Mathematical Reviews'Mathematical rewards [await] those who invest their mathematical energies in this beautiful pair of volumes.' Bulletin of the AMSPrize Winner Cambridge University Press congratulates Claire Voisin, winner of the 2007 Ruth Lyttle Satter Prize in Mathematics!Table of ContentsIntroduction. Part I. The Topology of Algebraic Varieties: 1. The Lefschetz theorem on hyperplane sections; 2. Lefschetz pencils; 3. Monodromy; 4. The Leray spectral sequence; Part II. Variations of Hodge Structure: 5. Transversality and applications; 6. Hodge filtration of hypersurfaces; 7. Normal functions and infinitesimal invariants; 8. Nori's work; Part III. Algebraic Cycles: 9. Chow groups; 10. Mumford' theorem and its generalisations; 11. The Bloch conjecture and its generalisations; References; Index.
£118.75
Cambridge University Press Computational Algebraic Geometry 58 London Mathematical Society Student Texts Series Number 58
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£94.99
Cambridge University Press Algebraic Geometry and Statistical Learning Theory 25 Cambridge Monographs on Applied and Computational Mathematics Series Number 25
Book SynopsisSure to be influential, this book lays the foundations for the use of algebraic geometry in statistical learning theory. Many widely used statistical models and learning machines applied to information science have a parameter space that is singular: mixture models, neural networks, HMMs, Bayesian networks, and stochastic context-free grammars are major examples. Algebraic geometry and singularity theory provide the necessary tools for studying such non-smooth models. Four main formulas are established: 1. the log likelihood function can be given a common standard form using resolution of singularities, even applied to more complex models; 2. the asymptotic behaviour of the marginal likelihood or 'the evidence' is derived based on zeta function theory; 3. new methods are derived to estimate the generalization errors in Bayes and Gibbs estimations from training errors; 4. the generalization errors of maximum likelihood and a posteriori methods are clarified by empirical process theory oTrade Review"Overall, the many insightful remarks and simple direct language make the book a pleasure to read." Shaowei Lin, Mathematical ReviewsTable of ContentsPreface; 1. Introduction; 2. Singularity theory; 3. Algebraic geometry; 4. Zeta functions and singular integral; 5. Empirical processes; 6. Singular learning theory; 7. Singular learning machines; 8. Singular information science; Bibliography; Index.
£73.14
Cambridge University Press Surveys in Combinatorics 2024
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£61.75
Cambridge University Press Lectures on Infinitary Model Theory
Book SynopsisThis book is the first modern introduction to the logic of infinitary languages in forty years, and is aimed at graduate students and researchers in all areas of mathematical logic. Connections between infinitary model theory and other branches of mathematical logic, and applications to algebra and algebraic geometry are both comprehensively explored.Table of ContentsIntroduction; Part I. Classical Results in Infinitary Model Theory: 1. Infinitary languages; 2. Back and forth; 3. The space of countable models; 4. The model existence theorem; 5. Hanf numbers and indiscernibles; Part II. Building Uncountable Models: 6. Elementary chains; 7. Vaught counterexamples; 8. Quasinimal excellence; Part III. Effective Considerations: 9. Effective descriptive set theory; 10. Hyperarithmetic sets; 11. Effective aspects of Lω1,ω; 12. Spectra of Vaught counterexamples; Appendix A. N1-free abelian groups; Appendix B. Admissibility; References; Index.
£105.45
Cambridge University Press 3264 and All That A Second Course in Algebraic
Book SynopsisThis book can form the basis of a second course in algebraic geometry. As motivation, it takes concrete questions from enumerative geometry and intersection theory, and provides intuition and technique, so that the student develops the ability to solve geometric problems. The authors explain key ideas, including rational equivalence, Chow rings, Schubert calculus and Chern classes, and readers will appreciate the abundant examples, many provided as exercises with solutions available online. Intersection is concerned with the enumeration of solutions of systems of polynomial equations in several variables. It has been an active area of mathematics since the work of Leibniz. Chasles' nineteenth-century calculation that there are 3264 smooth conic plane curves tangent to five given general conics was an important landmark, and was the inspiration behind the title of this book. Such computations were motivation for PoincarÃ's development of topology, and for many subsequent theories, so thTrade Review'… the book covers an important part of classical algebraic geometry with a modern point of view. It is indeed highly recommendable for a second (or a third) course in algebraic geometry| and more generally, for every mathematician interested in concrete algebraic geometry.' Arnaud Beauville, MathSciNetTable of ContentsIntroduction; 1. Introducing the Chow ring; 2. First examples; 3. Introduction to Grassmannians and lines in P3; 4. Grassmannians in general; 5. Chern classes; 6. Lines on hypersurfaces; 7. Singular elements of linear series; 8. Compactifying parameter spaces; 9. Projective bundles and their Chow rings; 10. Segre classes and varieties of linear spaces; 11. Contact problems; 12. Porteous' formula; 13. Excess intersections and the Chow ring of a blow-up; 14. The Grothendieck–Riemann–Roch theorem; Appendix A. The moving lemma; Appendix B. Direct images, cohomology and base change; Appendix C. Topology of algebraic varieties; Appendix D. Maps from curves to projective space; References; Index.
£44.92
Cambridge University Press Symmetry in Graphs
Book SynopsisThis is the first full-length book on the major theme of symmetry in graphs. Forming part of algebraic graph theory, this fast-growing field is concerned with the study of highly symmetric graphs, particularly vertex-transitive graphs, and other combinatorial structures, primarily by group-theoretic techniques. In practice the street goes both ways and these investigations shed new light on permutation groups and related algebraic structures. The book assumes a first course in graph theory and group theory but no specialized knowledge of the theory of permutation groups or vertex-transitive graphs. It begins with the basic material before introducing the field''s major problems and most active research themes in order to motivate the detailed discussion of individual topics that follows. Featuring many examples and over 450 exercises, it is an essential introduction to the field for graduate students and a valuable addition to any algebraic graph theorist''s bookshelf.Trade Review'The book is an excellent introduction to graph symmetry, assuming only first courses in each of group theory and graph theory. Illustrative and instructive examples of graphs with high symmetry are given along with motivating problems. The theory of group actions is interspersed throughout the book, as appropriate to the development of the graph story, and there are separate chapters treating different research directions, for example, vertex-transitive graphs and their automorphism groups, the Cayley Isomorphism Problem, and Hamiltonicity. The book provides a seamless entry for students and other interested people into this fascinating study of the interplay between symmetry and network theory, with extensive lists of exercises at the end of each chapter, and important research problems on graph symmetry discussed throughout the book, and especially in the final chapter.' Cheryl Praeger, University of Western Australia, Perth'Dobson, Malnič and Marušič have done us a real service. They offer a thorough treatment of graph symmetry, the first text book on the topic. What makes this even more useful is that their treatment is detailed, careful and gentle.' Chris Godsil, University of Waterloo, Ontario'A book like this is long overdue. It brings together a vast array of important and interesting material about graph symmetries, and is very well presented. Congratulations to the authors on a fine achievement.' Marston Conder, University of AucklandTable of Contents1. Introduction and constructions; 2. The Petersen graph, blocks, and actions of A5; 3. Some motivating problems; 4. Graphs with imprimitive automorphism group; 5. The end of the beginning; 6. Other classes of graphs; 7. The Cayley isomorphism problem; 8. Automorphism groups of vertex-transitive graphs; 9. Classifying vertex-transitive graphs; 10. Symmetric graphs; 11. Hamiltonicity; 12. Semiregularity; 13. Graphs with other types of symmetry: Half-arc-transitive graphs and semisymmetric graphs; 14. Fare you well; References; Author index; Index of graphs; Index of symbols;Index of terms.
£61.74
Cambridge University Press A Gentle Introduction to Homological Mirror
Book SynopsisOriginating in mathematical physics, homological mirror symmetry reveals deep connections between different areas of geometry and algebra. This book, which is aimed at graduate students, offers a self-contained and accessible introduction to the subject from the perspective of representation theory of algebras and quivers.Table of ContentsPart I. To A∞ and Beyond: 1. Categories; 2. Cohomology; 3. Higher products; 4. Quivers; Part II. A Glance through the Mirror: 5. Motivation from physics; 6. The A-side; 7. The B-side; 8. Mirror symmetry; Part III. Reflections on Surfaces: 9. Gluing; 10. Grading; 11. Stabilizing; 12. Deforming; References; Index.
£42.41
Cambridge University Press Complex Algebraic Threefolds
Book SynopsisThe first book on the explicit birational geometry of complex algebraic threefolds, this detailed text covers all the knowledge of threefolds needed to enter the field of higher dimensional birational geometry. Containing over 100 examples and many recent results, it is suitable for advanced graduate students as well as researchers.Trade Review'This book is an excellent introduction to the classification of complex algebraic threefolds. It includes a thorough modern treatment and a glimpse into many of the recent higher dimensional breakthroughs.' Christopher Hacon, University of UtahTable of Contents1. The minimal model program; 2. Singularities; 3. Divisorial contractions to points; 4. Divisorial contractions to curves; 5. Flips; 6. The Sarkisov category; 7. Conical fibrations; 8. Del Pezzo fibrations; 9. Fano threefolds; 10. Minimal models; References; Notation; Index.
£66.49
American Mathematical Society Linear Algebra for the Young Mathematician
Book SynopsisProvides a careful, thorough, and rigorous introduction to linear algebra. The book adopts a conceptual point of view, focusing on the notions of vector spaces and linear transformations, and it takes pains to provide proofs that bring out the essential ideas of the subject.Table of Contents Vector spaces: The basics Systems of linear equations Vector spaces Linear transformations More on vector spaces and linear transformations The determinant The structure of a linear transformation Jordan canonical form Vector spaces with additional structure: Forms on vector spaces Inner product spaces Fields Polynomials Normed vector spaces and questions of analysis A guide to further reading Index.
£74.10
