An Algebraic Introduction to Complex Projective Geometry

Commutative Algebra

Christian Peskine (Université de Paris VI (Pierre et Marie Curie))

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English

Cambridge University Press
16 April 2009

Mathematics & Sciences; Algebraic geometry

Series: Cambridge Studies in Advanced Mathematics

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.

By: Christian Peskine (Université de Paris VI (Pierre et Marie Curie))
Imprint: Cambridge University Press
Country of Publication: United Kingdom
Volume: No. 47
Dimensions: Height: 229mm, Width: 152mm, Spine: 14mm
Weight: 360g
ISBN: 9780521108478
ISBN 10: 0521108470
Series: Cambridge Studies in Advanced Mathematics
Pages: 244
Publication Date: 16 April 2009
Audience: Professional and scholarly , Undergraduate
Format: Paperback
Publisher's Status: Active