Integral Closure [electronic resource] : Rees Algebras, Multiplicities, Algorithms / by Wolmer Vasconcelos.

By: Vasconcelos, Wolmer [author.]
Contributor(s): SpringerLink (Online service)
Material type: TextTextSeries: Springer Monographs in Mathematics: Publisher: Berlin, Heidelberg : Springer Berlin Heidelberg, 2005Description: XII, 520 p. online resourceContent type: text Media type: computer Carrier type: online resourceISBN: 9783540265030Subject(s): Mathematics | Algebraic geometry | Commutative algebra | Commutative rings | Number theory | Mathematics | Commutative Rings and Algebras | Algebraic Geometry | Number TheoryAdditional physical formats: Printed edition:: No titleDDC classification: 512.44 LOC classification: QA251.3Online resources: Click here to access online
Contents:
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 -- HowTo.
In: Springer eBooksSummary: 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.
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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 -- HowTo.

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.

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