On the minimal model program for projective varieties with pseudo-effective tangent sheaf

TL;DR

This paper develops a theory of pseudo-effective sheaves on normal projective varieties and shows that varieties with pseudo-effective tangent sheaf can be decomposed into Fano and Q-abelian varieties using the minimal model program.

Contribution

It introduces a new framework for pseudo-effective sheaves and applies the minimal model program to classify varieties with pseudo-effective tangent sheaf.

Findings

Varieties with pseudo-effective tangent sheaf decompose into Fano and Q-abelian varieties.

Established a theory of pseudo-effective sheaves on normal projective varieties.

Applied the minimal model program to achieve the decomposition.

Abstract

In this paper, we develop a theory of pseudo-effective sheaves on normal projective varieties. As an application, by running the minimal model program, we show that projective klt varieties with pseudo-effective tangent sheaf can be decomposed into Fano varieties and Q-abelian varieties.