Minimal Free Resolutions over Complete Intersections: 2152 (Lecture Notes in Mathematics, 2152) - Softcover

Eisenbud, David; Peeva, Irena

Softcover

ISBN 10: 3319264362 ISBN 13: 9783319264363

Publisher: Springer, 2016

Synopsis

This book introduces a theory of higher matrix factorizations for regular sequences and uses it to describe the minimal free resolutions of high syzygy modules over complete intersections. Such resolutions have attracted attention ever since the elegant construction of the minimal free resolution of the residue field by Tate in 1957.

The theory extends the theory of matrix factorizations of a non-zero divisor, initiated by Eisenbud in 1980, which yields a description of the eventual structure of minimal free resolutions  over a hypersurface ring. Matrix factorizations have had many other uses in a wide range of mathematical fields, from singularity theory to mathematical physics.  

About this title

About the Author

The author taught at Brandeis University for twenty-seven years, with sabbatical time spent in Paris, Bonn, and Berkeley, and became Director of the Mathematical Sciences Research Institute in Berkeley in the Summer of 1997. At the same time he joined the faculty of UC Berkeley as Professor of Mathematics. In 2003 he became President of the American Mathematical Society. He currently serves on several editorial boards (Annals of Mathematics, Bulletin du Société Mathématique de France, Springer-Verlag's book series Algorithms and Computation in Mathematics).

From the Back Cover

This book introduces a theory of higher matrix factorizations for regular sequences and uses it to describe the minimal free resolutions of high syzygy modules over complete intersections. Such resolutions have attracted attention ever since the elegant construction of the minimal free resolution of the residue field by Tate in 1957.

The theory extends the theory of matrix factorizations of a non-zero divisor, initiated by Eisenbud in 1980, which yields a description of the eventual structure of minimal free resolutions over a hypersurface ring. Matrix factorizations have had many other uses in a wide range of mathematical fields, from singularity theory to mathematical physics.

Edition details

• Publisher: Springer
• Publication date: 2016
• Language: English
• ISBN 10: 3319264362
• ISBN 13: 9783319264363
• Binding: Paperback
• Edition number: 1
• Number of pages: 107