Description
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 Mathematicarum
Table 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.
