An Algebraic Introduction to Complex Projective Geometry

Commutative Algebra

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Hardcover | 1 July 1996

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244 Pages

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22.86 x 15.24 x 1.75

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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.

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

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Rings, homomorphisms, ideals
Modules
Noetherian rings and modules
Artinian rings and modules
Finitely generated modules over Noetherian rings
A first contact with homological algebra
Fractions
Integral extensions of rings
Algebraic extensions of rings
Noether's transformation lemma
Affine schemes
Morphisms of affine schemes
Zariski's main theorem
Integrally closed Noetherian rings
Weil divisors
Cartier divisors
Table of Contents provided by Publisher. All Rights Reserved.

An Algebraic Introduction to Complex Projective Geometry

Commutative Algebra

At a Glance

Hardcover

Industry Reviews

Shipping

How to return your order

Defective items

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