Integral Closure: Rees Algebras, Multiplicities, Algorithms / Edition 1

Integral Closure: Rees Algebras, Multiplicities, Algorithms / Edition 1

by Wolmer Vasconcelos
     
 

ISBN-10: 3540255400

ISBN-13: 9783540255406

Pub. Date: 06/01/2005

Publisher: Springer Berlin Heidelberg

"Integral Closure gives an account of theoretical and algorithmic developments on the integral closure of algebraic structures. These are shared concerns in commutative algebra, algebraic geometry, number theory and the computational aspects of these fields. The overall goal is to determine and analyze the equations of the assemblages of the set of solutions that…  See more details below

Overview

"Integral Closure gives an account of theoretical and algorithmic developments on the integral closure of algebraic structures. These are shared concerns in commutative algebra, algebraic geometry, number theory and the computational aspects of these fields. The overall goal is to determine and analyze the equations of the assemblages of the set of solutions that arise under various processes and algorithms. It gives a comprehensive treatment of Rees algebras and multiplicity theory - while pointing to applications in many other problem areas. Its main goal is to provide complexity estimates by tracking numerically invariants of the structures that may occur." This book is intended for graduate students and researchers in the fields mentioned above. It contains, besides exercises aimed at giving insights, numerous research problems motivated by the developments reported.

Product Details

ISBN-13:
9783540255406
Publisher:
Springer Berlin Heidelberg
Publication date:
06/01/2005
Series:
Springer Monographs in Mathematics Series
Edition description:
2005
Pages:
520
Product dimensions:
9.21(w) x 6.14(h) x 1.19(d)

Table of Contents

Preface.- Introduction.- Numerical Invariants of a Rees Algebra.- Hilbert Functions and Multiplicities.- Depth and Cohomology of Rees Algebras.- Divisors of a Rees Algebra.- Koszul Homology.- Integral Closure of Algebras.- Integral Closure and Normalization of Ideals.- Integral Closure of Modules.- How To.- References.- Notation and Terminology.- Index.

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