Mather-Jacobian singularities under generic linkage

TL;DR

This paper proves that Mather-Jacobian singularities, including MJ-canonical and MJ-log canonical types, are preserved under generic linkage, impacting the understanding of singularity behavior and minimal log discrepancies.

Contribution

It establishes the preservation of Mather-Jacobian singularities under generic linkage, a new result in the study of algebraic singularities.

Findings

MJ-singularities are preserved under generic linkage

Results on minimal log discrepancies under generic linkage

Extension of singularity classification under 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.