A concise introduction to algebraic varieties
Author(s)
Bibliographic Information
A concise introduction to algebraic varieties
（Graduate studies in mathematics, 216）
American Mathematical Society, c2021
- : hardcover
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Note
Includes bibliographical references (p. 247-249) and indexes
Description and Table of Contents
Description
A Concise Introduction to Algebraic Varieties is designed for a one-term introductory course on algebraic varieties over an algebraically closed field, and it provides a solid basis for a course on schemes and cohomology or on specialized topics, such as toric varieties and moduli spaces of curves. The book balances generality and accessibility by presenting local and global concepts, such as nonsingularity, normality, and completeness using the language of atlases, an approach that is most commonly associated with differential topology. The book concludes with a discussion of the Riemann-Roch theorem, the Brill-Noether theorem, and applications.
The prerequisites for the book are a strong undergraduate algebra course and a working familiarity with basic point-set topology. A course in graduate algebra is helpful but not required. The book includes appendices presenting useful background in complex analytic topology and commutative algebra and provides plentiful examples and exercises that help build intuition and familiarity with algebraic varieties.
Table of Contents
Introduction: An overview of algebraic geometry through the lens of plane curves
Affine algebraic varieties
Regular functions and morphisms
Singularities
Abstract varieties via atlases
Projective varieties
Nonsingular curves and complete varieties
Divisors on nonsingular curves
Differential forms
An invitation to the theory of algebraic curves
Complex varieties and the analytic topology
A roadmap through algebra
Bibliography
Index of notation
Index
by "Nielsen BookData"
