Structure theorem for projective klt pairs with nef anti-canonical divisor

Shin-ichi Matsumura, Juanyong Wang

Published 2021-05-29Version 1

In this paper, we establish a structure theorem for projective Kawamata log terminal (klt) pairs $(X,\Delta)$ with nef anti-log canonical divisor; specifically, we prove that up to replacing $X$ with a finite quasi-\'etale cover, $X$ admits a locally trivial rationally connected fibration onto a projective klt variety with numerically trivial canonical divisor. Our structure theorem generalizes previous works for smooth projective varieties and reduces the structure problem to the singular Beauville-Bogomolov decomposition for Calabi-Yau varieties. As an application, the projective varieties of klt Calabi-Yau type, which naturally appear as an outcome of the Log Minimal Model Program, are decomposed into building block varieties, namely, rationally connected varieties and Calabi-Yau varieties.