Description

Book Synopsis
Presents a readable and accessible introductory course in algebraic geometry, with most of the fundamental classical results presented with complete proofs. An emphasis is placed on developing connections between geometric and algebraic aspects of the theory. Differences between the theory in characteristic $0$ and positive characteristic are emphasized.

Table of Contents
  • A crash course in commutative algebra
  • Affine varieties
  • Projective varieties
  • Regular and rational maps of quasi-projective varieties
  • Products
  • The blow-up of an ideal
  • Finite maps of quasi-projective varieties
  • Dimension of quasi-projective algebraic sets
  • Zariski's main theorem
  • Nonsingularity
  • Sheaves
  • Applications to regular and rational maps
  • Divisors
  • Differential forms and the canonical divisor
  • Schemes
  • The degree of a projective variety
  • Cohomology
  • Curves
  • An introduction to intersection theory
  • Surfaces
  • Ramification and etale maps
  • Bertini's theorem and general fibers of maps
  • Bibliography
  • Index.

    Introduction to Algebraic Geometry

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      £110.70

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      Order before 4pm today for delivery by Tue 16 Jun 2026.

      A Hardback by Steven Dale Cutkosky

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        Publisher: American Mathematical Society
        Publication Date: 30/07/2018
        ISBN13: 9781470435189, 978-1470435189
        ISBN10: 1470435187
        Also in:
        Mathematics Algebraic geometry Not Just Books Stationery

        Description

        Book Synopsis
        Presents a readable and accessible introductory course in algebraic geometry, with most of the fundamental classical results presented with complete proofs. An emphasis is placed on developing connections between geometric and algebraic aspects of the theory. Differences between the theory in characteristic $0$ and positive characteristic are emphasized.

        Table of Contents
        • A crash course in commutative algebra
        • Affine varieties
        • Projective varieties
        • Regular and rational maps of quasi-projective varieties
        • Products
        • The blow-up of an ideal
        • Finite maps of quasi-projective varieties
        • Dimension of quasi-projective algebraic sets
        • Zariski's main theorem
        • Nonsingularity
        • Sheaves
        • Applications to regular and rational maps
        • Divisors
        • Differential forms and the canonical divisor
        • Schemes
        • The degree of a projective variety
        • Cohomology
        • Curves
        • An introduction to intersection theory
        • Surfaces
        • Ramification and etale maps
        • Bertini's theorem and general fibers of maps
        • Bibliography
        • Index.

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