An Algebraic Introduction to Complex Projective Geometry
Commutative Algebra Commutative Algebra Bk. 1
By (author) Christian Peskine
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Algebraic Introduction to Complex Projective Geometry by Christian Peskine
Book DescriptionIn 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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Book DetailsISBN: 9780521480727
(228mm x 152mm x 17mm)
Imprint: Cambridge University Press
Publisher: Cambridge University Press
Publish Date: 2-May-1996
Country of Publication: United Kingdom
Books By Author Christian Peskine
Algebraic Introduction to Complex Projective Geometry, Paperback (April 2009)
An excellent textbook for those who seek an efficient and rapid introduction to the geometric applications of commutative algebra.
Complex Projective Geometry, Paperback (July 1992)» View all books by Christian Peskine
A volume of papers describing new methods in algebraic geometry.
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