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An Algebraic Introduction to Complex Projective Geometry: Commutative Algebra - Couverture rigide

Peskine, Christian

 
9780521480727: An Algebraic Introduction to Complex Projective Geometry: Commutative Algebra
Couverture rigide
ISBN 10 : 0521480728 ISBN 13 : 9780521480727
Editeur : Cambridge University Press, 1996

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.

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Présentation de l'éditeur

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.

Revue de presse

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

Les informations fournies dans la section « A propos du livre » peuvent faire référence à une autre édition de ce titre.

Éditeur
Cambridge University Press
Date d'édition
1996
Langue
anglais
ISBN 10 
0521480728
ISBN 13 
9780521480727
Reliure
Relié
Nombre de pages
244
Coordonnées du fabricant
Cambridge University Press
https://www.cambridge.org/

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