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Cambridge Studies in Advanced Mathematics An Algebraic Introduction to Complex Projective Geometry: Commutative Algebra

by Christian (Universite de Paris VI (Pierre et Marie Curie)) Peskine

Cambridge Studies in Advanced Mathematics An Algebraic Introduction to Complex Projective Geometry: Commutative Algebra Synopsis

In this introduction to commutative algebra, the author 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. In the first part, the general theory of Noetherian rings and modules is developed. A certain amount of homological algebra is included, and rings and modules of fractions are emphasised, as preparation for working with sheaves. In the second part, the central objects are polynomial rings in several variables with coefficients in the field of complex numbers. After Noether's normalisation lemma and Hilbert's Nullstellensatz, affine complex schemes and their morphisms are introduced; Zariski's main theorem and Chevalley's semi-continuity theorem are then proved. Finally, a 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.

Cambridge Studies in Advanced Mathematics An Algebraic Introduction to Complex Projective Geometry: Commutative Algebra Press Reviews

'... a detailed study ... a solid background.' L'Enseignement Mathematique 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

Book Information

ISBN: 9780521480727
Publication date: 2nd May 1996
Author: Christian (Universite de Paris VI (Pierre et Marie Curie)) Peskine
Publisher: Cambridge University Press
Format: Hardback
Pagination: 244 pages
Categories: Algebraic geometry, Groups & group theory,

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