A Concise Introduction to Algebraic Varieties

Brian Osserman

ISBN 10: 1470466651 / ISBN 13: 9781470466657

Editore: American Mathematical Society, US, 2022

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. Codice articolo LU-9781470466657

Riassunto:

Osserman presents a textbook for a one-semester or one-quarter course introducing the theory of abstract algebraic varieties over algebraically closed fields. It provides a foundation in the basic properties of varieties, preparing readers either for learning a more specialized area such as toric varieties or modulii of curves, or for moving on to the theory of schemes. Among his topics are affine algebraic varieties, regular functions and morphisms, abstract varieties via atlases, divisors on non-singular curves, and an invitation to the theory of algebraic curves. Annotation ©2022 Ringgold, Inc., Portland, OR (protoview.com)

Dati bibliografici

Titolo: A Concise Introduction to Algebraic Varieties
Casa editrice: American Mathematical Society, US
Data di pubblicazione: 2022
Legatura: Paperback
Condizione: New