An Algebraic Introduction to Complex Projective Geometry
Commutative Algebra
$169.00 (C)
Part of Cambridge Studies in Advanced Mathematics
- Author: Christian Peskine, Université de Paris VI (Pierre et Marie Curie)
- Date Published: May 1996
- availability: Available
- format: Hardback
- isbn: 9780521480727
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169.00
(C)
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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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Reviews & endorsements
"Useful, apt advice and numerous expository niceties make this compact volume a pleasure to read. Highly recommended." Choice
See more reviews"...a good and systematic introduction to complex projective geometry....an excellent textbook." Mathematical Reviews
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×Product details
- Date Published: May 1996
- format: Hardback
- isbn: 9780521480727
- length: 244 pages
- dimensions: 237 x 157 x 19 mm
- weight: 0.454kg
- availability: Available
Table of Contents
1. Rings, homomorphisms, ideals
2. Modules
3. Noetherian rings and modules
4. Artinian rings and modules
5. Finitely generated modules over Noetherian rings
6. A first contact with homological algebra
7. Fractions
8. Integral extensions of rings
9. Algebraic extensions of rings
10. Noether's normalisation lemma
11. Affine schemes
12. Morphisms of affine schemes
13. Zariski's main theorem
14. Integrally closed Noetherian rings
15. Weil divisors
16. Cartier divisors
Subject index
Symbols index.
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