Matrix factorizations in higher codimension

We observe that there is an equivalence between the singularity category of an affine complete intersection and the homotopy category of matrix factorizations over a related scheme. This relies in part on a theorem of Orlov. Using this equivalence, we give a geometric construction of the ring of coh...

Full description

Saved in:
Bibliographic Details
Published in:arXiv.org 2012-05
Main Authors: Burke, Jesse, Walker, Mark E
Format: Article
Language:English
Subjects:
Equivalence
Homology
Hyperspaces
Operators (mathematics)
Rings (mathematics)
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary:We observe that there is an equivalence between the singularity category of an affine complete intersection and the homotopy category of matrix factorizations over a related scheme. This relies in part on a theorem of Orlov. Using this equivalence, we give a geometric construction of the ring of cohomology operators, and a generalization of the theory of support varieties, which we call stable support sets. We settle a question of Avramov about which stable support sets can arise for a given complete intersection ring. We also use the equivalence to construct a projective resolution of a module over a complete intersection ring from a matrix factorization, generalizing the well-known result in the hypersurface case.
ISSN:2331-8422