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OverviewThis book is an introduction to the geometry of complex algebraic varieties. It is intended for students who have learned algebra, analysis, and topology, as taught in standard undergraduate courses. So it is a suitable text for a beginning graduate course or an advanced undergraduate course. The book begins with a study of plane algebraic curves, then introduces affine and projective varieties, going on to dimension and construcibility. $\mathcal{O}$-modules (quasicoherent sheaves) are defined without reference to sheaf theory, and their cohomology is defined axiomatically. The Riemann-Roch Theorem for curves is proved using projection to the projective line. Some of the points that aren't always treated in beginning courses are Hensel's Lemma, Chevalley's Finiteness Theorem, and the Birkhoff-Grothendieck Theorem. The book contains extensive discussions of finite group actions, lines in $\mathbb{P}^3$, and double planes, and it ends with applications of the Riemann-Roch Theorem. Full Product DetailsAuthor: Michael ArtinPublisher: American Mathematical Society Imprint: American Mathematical Society Weight: 0.363kg ISBN: 9781470468484ISBN 10: 1470468484 Pages: 322 Publication Date: 30 December 2022 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 ContentsPlane curves Affine algebraic geometry Projective algebraic geometry Integral morphisms Structure of varieties in the Zariski topology Modules Cohomology The Riemann-Roch Theorem for curves Background Glossary Index of notation Bibliography IndexReviewsAuthor InformationMichael Artin, Massachusetts Institute of Technology, Cambridge, MA. Tab Content 6Author Website:Countries AvailableAll regions |
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