Algebraic Geometry: Notes on a Course - Couverture souple

Artin, Michael

 
9781470471118: Algebraic Geometry: Notes on a Course
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.

Les informations fournies dans la section « Synopsis » peuvent faire référence à une autre édition de ce titre.

À propos de l?auteur

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

Les informations fournies dans la section « A propos du livre » peuvent faire référence à une autre édition de ce titre.

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