Matrix factorizations and singularity categories in codimension two
Matrix factorizations and singularity categories in codimension two
复制标题
余维二中的矩阵分解和奇点类别
DOI：
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发表时间：
2018
影响因子：
1
通讯作者：
Matthew Mastroeni
中科院分区：
文献类型：
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作者：
Matthew Mastroeni
2004 年的奥尔洛夫定理指出，仿射超曲面 Y 上的矩阵分解的同伦范畴相当于 Y 上相干滑轮的有界派生范畴的商，称为奇点范畴。随后，伯克和沃克将这一结果推广到完成更高余维的交集。 2013 年，Eisenbud 和 Peeva 引入了任意余维矩阵分解的概念。作为协调这两种方法的第一步，本文描述了如何从余维两个矩阵分解到相应完全交集的奇点类别构造函子。
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 note describes how to construct a functor from codimension two matrix factorizations to the singularity category of the corresponding complete intersection.