Algebraic Geometry: Notes on a Course - Couverture souple

Artin, Michael

Couverture souple

ISBN 10 : 1470471116 ISBN 13 : 9781470471118

Editeur : American Mathematical Society, 2022

Synopsis

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.

A propos du livre

À propos de l?auteur

Michael Artin, Massachusetts Institute of Technology, Cambridge, MA.

Détails de l'édition

• Éditeur: American Mathematical Society
• Date d'édition: 2022
• Langue: anglais
• ISBN 10: 1470471116
• ISBN 13: 9781470471118
• Reliure: Broché
• Nombre de pages: 322
• Coordonnées du fabricant: non disponible
• Personne responsable: non disponible