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9781470471118 Academic Inspection Copy

Algebraic Geometry

Notes on a Course
  • ISBN-13: 9781470471118
  • Publisher: AMERICAN MATHEMATICAL SOCIETY
    Imprint: AMERICAN MATHEMATICAL SOCIETY
  • By Michael Artin
  • Price: AUD $219.00
  • Stock: 0 in stock
  • Availability: This book is temporarily out of stock, order will be despatched as soon as fresh stock is received.
  • Local release date: 28/02/2023
  • Format: Paperback 322 pages Weight: 271g
  • Categories: Algebraic geometry [PBMW]
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This 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.
Michael Artin, Massachusetts Institute of Technology, Cambridge, MA.
Plane 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 Index
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