The Nonvanishing Problem for varieties with nef anticanonical bundle

Vladimir Lazić; Shin-ichi Matsumura; Thomas Peternell; Nikolaos Tsakanikas; Zhixin Xie

doi:10.4171/dm/936

JournalsdmVol. 28, No. 6pp. 1393–1440

The Nonvanishing Problem for varieties with nef anticanonical bundle

Vladimir Lazić
Universität des Saarlandes, Saarbrücken, Germany
Shin-ichi Matsumura
Tohoku University, Sendai, Japan
Thomas Peternell
Universität Bayreuth, Bayreuth, Germany
Nikolaos Tsakanikas
École Polytechnique Fédérale de Lausanne, Lausanne, Switzerland
Zhixin Xie
Université de Lorraine, Nancy, France

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Abstract

We prove that if $(X, Δ)$ is a threefold pair with mild singularities such that $- (K_{X} + Δ)$ is nef, then the numerical class of $- (K_{X} + Δ)$ is effective.

Cite this article

Vladimir Lazić, Shin-ichi Matsumura, Thomas Peternell, Nikolaos Tsakanikas, Zhixin Xie, The Nonvanishing Problem for varieties with nef anticanonical bundle. DM 28 (2023), no. 6, pp. 1393–1440

DOI 10.4171/DM/936