Algebraic Geometry by Michael Artin

Algebraic Geometry by Michael Artin

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.

SKU	Unavailable
ISBN 13	9781470471118
ISBN 10	1470471116
Title	Algebraic Geometry
Author	Michael Artin
Series	Graduate Studies In Mathematics
Condition	Unavailable
Binding Type	Paperback
Publisher	American Mathematical Society
Year published	2022-11-30
Number of pages	322
Cover note	Book picture is for illustrative purposes only, actual binding, cover or edition may vary.
Note	Unavailable