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Matrix factorizations and singularity categories in codimension two

Author: Matthew Mastroeni
Journal: Proc. Amer. Math. Soc. 146 (2018), 4605-4617
MSC (2010): Primary 13C40; Secondary 13D02
Published electronically: June 28, 2018
MathSciNet review: 3856131
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Abstract: A theorem of Orlov from 2004 states that the homotopy category of matrix factorizations on an affine hypersurface $ Y$ is equivalent to a quotient of the bounded derived category of coherent sheaves on $ Y$ called the singularity category. This result was subsequently generalized to complete intersections of higher codimension by Burke and Walker. In 2013, Eisenbud and Peeva introduced the notion of matrix factorizations in arbitrary codimension. As a first step towards reconciling these two approaches, this paper describes how to construct a functor from codimension two matrix factorizations to the singularity category of the corresponding complete intersection.

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Matthew Mastroeni
Affiliation: Department of Mathematics, University of Illinois, 1409 W. Green Street, Urbana, Illinois 61801

Received by editor(s): August 8, 2017
Received by editor(s) in revised form: February 16, 2018
Published electronically: June 28, 2018
Additional Notes: The author also acknowledges support from National Science Foundation grant DMS 08-38434 “EMSW21-MCTP: Research Experience for Graduate Students”.
Communicated by: Irena Peeva
Article copyright: © Copyright 2018 American Mathematical Society