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OverviewA 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. Full Product DetailsAuthor: Brian OssermanPublisher: American Mathematical Society Imprint: American Mathematical Society ISBN: 9781470460136ISBN 10: 1470460130 Pages: 256 Publication Date: 31 January 2023 Audience: Professional and scholarly , Professional & Vocational Format: Hardback Publisher's Status: Active Availability: In Print  This item will be ordered in for you from one of our suppliers. Upon receipt, we will promptly dispatch it out to you. For in store availability, please contact us. Table of ContentsIntroduction: 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 IndexReviewsAuthor InformationTab Content 6Author Website:Countries AvailableAll regions |
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