Mather-Jacobian singularities under generic linkage

Abstract

In this paper, we prove that Mather-Jacobian (MJ) singularities are preserved under the process of generic linkage. More precisely, let $X$ be a variety with MJ-canonical (resp. MJ-log canonical) singularities. Then a generic link of $X$ is also MJ-canonical (resp. MJ-log canonical). This further leads us to a result on minimal log discrepancies under generic linkage.