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Strictly nef divisors on singular threefolds

Juanyong Wang

https://orcid.org/0000-0003-2744-4624

Institute of Mathematics, Chinese Academy of Sciences, Beijing 100190, P. R. China

E-mail Address: [email protected]

Corresponding author.

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and

Guolei Zhong

https://orcid.org/0000-0001-7792-9529

Department of Mathematics, National University of Singapore, 10 Lower Kent Ridge Road, Singapore 119076, Republic of Singapore

E-mail Address: [email protected]

Current address: Center for Complex Geometry, Institute for Basic Science (IBS), 55 Expo-ro, Yuseong-gu, Daejeon, 34126, Republic of Korea.

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https://doi.org/10.1142/S0129167X2450054XCited by:0 (Source: Crossref)

Abstract

Let $X$ be a normal projective variety with klt singularities and $L_{X}$ a strictly nef $ℚ$ -divisor on $X$ . In this paper, we study the singular version of Serrano’s conjecture, i.e. the ampleness of $K_{X} + t L_{X}$ for $t ≫ 1$ . We show that, if $X$ is a $ℚ$ -factorial Gorenstein terminal threefold, then $K_{X} + t L_{X}$ is ample for $t ≫ 1$ unless $X$ is a weak Calabi–Yau variety (i.e. the canonical divisor $K_{X}$ is a $ℚ$ -torsion and the augmented irregularity $q^{\circ} (X)$ vanishes) with $L_{X} \cdot c_{2} (X) = 0$ .

Communicated by Jungkai A. Chen

Keywords:

AMSC: 14E30, 14J30

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