Minimal Free Resolutions over Complete Intersections

Nonfiction, Science & Nature, Mathematics, Geometry, Algebra
Cover of the book Minimal Free Resolutions over Complete Intersections by David Eisenbud, Irena Peeva, Springer International Publishing
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Author: David Eisenbud, Irena Peeva ISBN: 9783319264370
Publisher: Springer International Publishing Publication: March 8, 2016
Imprint: Springer Language: English
Author: David Eisenbud, Irena Peeva
ISBN: 9783319264370
Publisher: Springer International Publishing
Publication: March 8, 2016
Imprint: Springer
Language: English

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.  

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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.  

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