Matrix factorizations and singularity categories in codimension two

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.