Potential log canonical centers

TL;DR

This paper provides criteria for constructing boundary divisors on a variety so that a given subvariety becomes a log canonical center, and conditions under which the pair has log canonical singularities.

Contribution

It establishes sufficient conditions for a subvariety to be a log canonical center and for the pair to have log canonical singularities, advancing the understanding of singularity structures.

Findings

Criteria for existence of boundary divisors making Z a log canonical center

Conditions under which the pair (X, Δ) has log canonical singularities

Method to construct such divisors under specific hypotheses

Abstract

Given an ambient variety $X$ and a fixed subvariety $Z$ we give sufficient conditions for the existence of a boundary $\Delta$ such that $Z$ is a log canonical center for the pair $(X, \Delta)$. We also show that under some additional hypotheses $\Delta$ can be chosen such that $(X, \Delta)$ has log canonical singularities.