An Algebraic Introduction to Complex Projective Geometry: Commutative Algebra (Paperback) (ISBN-13: 9780521108478)

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.

Author: Christian Peskine
ISBN-10: 0521108470
ISBN-13: 9780521108478
Publisher: Cambridge University Press
Language: English
Published: 04/09/2009
Pages: 244
Format: Paperback
Weight: 0.80lbs
Size: 9.00h x 6.00w x 0.55d