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Science/Engineering Twenty-Four Hours of Local Cohomology

Posted on 2010-03-16




Name:Science/Engineering Twenty-Four Hours of Local Cohomology
ASIN/ISBN:0821841262
Language:English
File size:1.7 Mb
Publish Date: 2007
ISBN: 0821841262
File Type: PDF
Pages: 282 pages
File Size: 1,7 MB
Other Info: American Mathematical Society
   Science/Engineering Twenty-Four Hours of Local Cohomology

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Srikanth B. Iyengar, Graham J. Leuschke, Anton Leykin, Claudia Miller, Ezra Miller, "Twenty-Four Hours of Local Cohomology"

This book is aimed to provide an introduction to local cohomology which takes cognizance of the breadth of its interactions with other areas of mathematics. It covers topics such as the number of defining equations of algebraic sets, connectedness properties of algebraic sets, connections to sheaf cohomology and to de Rham cohomology, Gröbner bases in the commutative setting as well as for $D$-modules, the Frobenius morphism and characteristic $p$ methods, finiteness properties of local cohomology modules, semigroup rings and polyhedral geometry, and hypergeometric systems arising from semigroups. The book begins with basic notions in geometry, sheaf theory, and homological algebra leading to the definition and basic properties of local cohomology. Then it develops the theory in a number of different directions, and draws connections with topology, geometry, combinatorics, and algorithmic aspects of the subject.

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