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

Shin-ichi Matsumura; Juanyong Wang

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arXiv · 2105.14308

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

Shin-ichi Matsumura·Juanyong Wang

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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-\'etale 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.

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BibTeX RIS

Shin-ichi Matsumura, Juanyong Wang. 2021-05-29. Structure theorem for projective klt pairs with nef anti-canonical divisor. https://arxiv.org/abs/2105.14308

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