Algebraic geometry : notes on a course

Bibliographic Information

Algebraic geometry : notes on a course

Michael Artin

(Graduate studies in mathematics, 222)

American Mathematical Society, c2022

  • : hardcover

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Note

Includes bibliographical references (p. 313-314) and index

Description and Table of Contents

Description

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.

Table of Contents

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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Details

  • NCID
    BC17004773
  • ISBN
    • 9781470468484
  • LCCN
    2022012175
  • Country Code
    us
  • Title Language Code
    eng
  • Text Language Code
    eng
  • Place of Publication
    Providence, R.I.
  • Pages/Volumes
    x, 318 p.
  • Size
    27 cm
  • Classification
  • Subject Headings
  • Parent Bibliography ID
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