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Study An Algebraic Introduction to Complex Projective Geometry: Commutative Algebra (Cambridge Studies in Advanced Mathematics)

Posted on 2010-03-16




Name:Study An Algebraic Introduction to Complex Projective Geometry: Commutative Algebra (Cambridge Studies in Advanced Mathematics)
ASIN/ISBN:0521108470
Language:English
File size:5.7 Mb
Language: English
Publish Date: 2009-04-09
ISBN: 0521108470
Pages: 244 pages
File Type: PDF
File Size: 5,7 MB
Other Info: Cambridge University Press
   Study An Algebraic Introduction to Complex Projective Geometry: Commutative Algebra (Cambridge Studies in Advanced Mathematics)



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Christian Peskine "An Algebraic Introduction to Complex Projective Geometry: Commutative Algebra (Cambridge Studies in Advanced Mathematics)"

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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