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

Abstract

In this paper, we establish a structure theorem for projective klt pairs $(X,\Delta )$ with nef anti-log canonical divisor; specifically, we prove that, up to replacing $X$ with a finite quasi-étale cover, $X$ admits a locally trivial rationally connected fibration onto a projective klt variety with numerically trivial canonical divisor. This structure theorem generalizes previous works for smooth projective varieties and reduces several structure problems to the singular Beauville-Bogomolov decomposition for Calabi-Yau varieties. As an application, 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: rationally connected varieties and Calabi-Yau varieties.

arXiv comment42 pages, the proof of Theorem 3.2 simplified

References in corpus (6)

• Étale fundamental groups of Kawamata log terminal spaces, flat sheaves, and quotients of Abelian varieties
• Generic positivity and applications to hyperbolicity of moduli spaces
• Projective klt pairs with nef anti-canonical divisor
• Orbifold slope-rational connectedness
• Pseudo-effective and numerically flat reflexive sheaves
• The Bogomolov-Beauville-Yau Decomposition for Klt Projective Varieties with Trivial First Chern Class -Without Tears-

Cited by in corpus (2)

• The Nonvanishing problem for varieties with nef anticanonical bundle
• On the minimal model program for projective varieties with pseudo-effective tangent sheaf