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An Algebraic Introduction to Complex Projective Geometry: Commut

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Características del artículo

Estado
En muy buen estado: Libro que se ha leído y que no tiene un aspecto nuevo, pero que está en un ...
Title
An Algebraic Introduction to Complex Projective Geometry: Commut
ISBN
9780521480727

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Product Identifiers

Publisher
Cambridge University Press
ISBN-10
0521480728
ISBN-13
9780521480727
eBay Product ID (ePID)
536518

Product Key Features

Number of Pages
244 Pages
Publication Name
Algebraic Introduction to Complex Projective Geometry Vol. 1 : Commutative Algebra
Language
English
Publication Year
1996
Subject
Algebra / General, Geometry / Algebraic, Complex Analysis
Type
Textbook
Subject Area
Mathematics
Author
Christian Peskine
Series
Cambridge Studies in Advanced Mathematics Ser.
Format
Hardcover

Dimensions

Item Height
0.7 in
Item Weight
16 Oz
Item Length
9.3 in
Item Width
6.2 in

Additional Product Features

Intended Audience
Scholarly & Professional
LCCN
94-046980
Reviews
"Useful, apt advice and numerous expository niceties make this compact volume a pleasure to read. Highly recommended." Choice, "...a good and systematic introduction to complex projective geometry....an excellent textbook." Mathematical Reviews
Dewey Edition
20
TitleLeading
An
Series Volume Number
Series Number 47
Dewey Decimal
516/.5
Table Of Content
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.
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., An excellent textbook for those who seek an efficient and rapid introduction to the geometric applications of commutative algebra., 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., This is an excellent textbook for those who seek an efficient and rapid introduction to the geometric applications of commutative algebra. 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.
LC Classification Number
QA564 .P47 1996

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