Twenty-Four Hours of Local Cohomology: 87 (Graduate Studies in Mathematics) - Softcover

Iyengar, Srikanth B.; Leuschke, Graham J.; Leykin, Anton; Miller, Claudia; Miller, Ezra

Softcover

ISBN 10: 1470471590 ISBN 13: 9781470471590

Publisher: American Mathematical Society, 2007

Synopsis

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, Grobner 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.

About this title

About the Author

Srikanth B. Iyengar, University of Nebraska, Lincoln, NE.

Graham J. Leuschke, Syracuse University, NY.

Anton Leykin, Institute for Mathematics and Its Applications, Syracuse, NY.

Claudia Miller, Syracuse University, NY.

Ezra Miller, University of Minnesota, Minneapolis, MN.

Anurag K. Singh, University of Utah, Salt Lake City, UT.

Uli Walther, Purdue University, West Lafayette, IN.

Edition details

• Publisher: American Mathematical Society
• Publication date: 2007
• Language: English
• ISBN 10: 1470471590
• ISBN 13: 9781470471590
• Binding: Paperback
• Number of pages: 282