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.
- ISBN13 9783319264363
- Publish Date 9 March 2016
- Publish Status Active
- Publish Country CH
- Imprint Springer International Publishing AG
- Edition 1st ed. 2016
- Format Paperback
- Pages 107
- Language English