On the radius of the category of extensions of matrix factorizations

Abstract

Let $S$ be a commutative noetherian ring. The extensions of matrix factorizations of non-zerodivisors $x_1,\dots,x_n$ of $S$ form a full subcategory of finitely generated modules over the quotient ring $S/(x_1\cdots x_n)$. In this paper, we investigate the radius (in the sense of Dao and Takahashi) of this full subcategory. As an application, we obtain an upper bound of the dimension (in the sense of Rouquier) of the singularity category of a local hypersurface of dimension one, which refines a recent result of Kawasaki, Nakamura and Shimada.