An Algebraic Introduction to Complex Projective Geometry

Peskine Christian Christian Peskine

ISBN 10: 0521108470 / ISBN 13: 9780521108478

Published by Cambridge University Press, 2009

About this Item

PRINT ON DEMAND pp. 244.

Seller Inventory # 18531494

Bibliographic Details

• Title: An Algebraic Introduction to Complex Projective Geometry
• Publisher: Cambridge University Press
• Publication Date: 2009
• Language: English
• ISBN 10: 0521108470
• ISBN 13: 9780521108478
• Binding: Soft cover
• Condition: New

About this title

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.

Review

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