An Algebraic Introduction to Complex Projective Geometry: Commutative Algebra (Cambridge Studies in Advanced Mathematics, Series Number 47) - Hardcover

Peskine, Christian

Hardcover

ISBN 10: 0521480728 ISBN 13: 9780521480727

Publisher: Cambridge University Press, 1996

Synopsis

In this introduction to commutative algebra, the author choses a route that leads the reader through the essential ideas, without getting embroiled in technicalities. He takes the reader quickly to the fundamentals of complex projective geometry, requiring only a basic knowledge of linear and multilinear algebra and some elementary group theory. The author divides the book into three parts. In the first, he develops the general theory of noetherian rings and modules. He includes a certain amount of homological algebra, and he emphasizes rings and modules of fractions as preparation for working with sheaves. In the second part, he discusses polynomial rings in several variables with coefficients in the field of complex numbers. After Noether's normalization lemma and Hilbert's Nullstellensatz, the author introduces affine complex schemes and their morphisms; he then proves Zariski's main theorem and Chevalley's semi-continuity theorem. Finally, the author's detailed study of Weil and Cartier divisors provides a solid background for modern intersection theory. This is an excellent textbook for those who seek an efficient and rapid introduction to the geometric applications of commutative algebra.

About this title

Book Description

In this introduction to commutative algebra, the author has chosen a route that leads the beginning student through the essential ideas, without getting embroiled in technicalities. The route chosen takes the reader quickly to the fundamental concepts for understanding complex projective geometry, the only prerequisites being a basic knowledge of linear and multilinear algebra and some elementary group theory.This is an excellent textbook for those who seek an efficient and rapid introduction to the geometric applications of commutative algebra.

Review

"Useful, apt advice and numerous expository niceties make this compact volume a pleasure to read. Highly recommended." Choice

"...a good and systematic introduction to complex projective geometry....an excellent textbook." Mathematical Reviews

Edition details

• Publisher: Cambridge University Press
• Publication date: 1996
• Language: English
• ISBN 10: 0521480728
• ISBN 13: 9780521480727
• Binding: Hardcover
• Edition number: 1
• Number of pages: 244