Potentially non-klt locus and its applications

TL;DR

This paper introduces the concept of potentially non-klt locus for certain algebraic varieties, providing new insights into their structure and applications to characterizations of Fano type and rational connectedness.

Contribution

It defines potentially klt pairs and potentially non-klt locus, establishing their properties and applications in classifying algebraic varieties.

Findings

Characterization of Fano type varieties using potentially non-klt locus

Improved results on rational connectedness of uniruled varieties

Basic properties of potentially non-klt locus established

Abstract

We introduce the notion of potentially klt pairs for normal projective varieties with pseudoeffective anticanonical divisor. The potentially non-klt locus is a subset of $X$ which is birationally transformed precisely into the non-klt locus on a $-K_X$-minimal model of $X$. We prove basic properties of potentially non-klt locus in comparison with those of classical non-klt locus. As applications, we give a new characterization of varieties of Fano type, and we also improve results on the rational connectedness of uniruled varieties with pseudoeffective anticanonical divisor.