Strictly nef divisors on singular threefolds
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arXiv
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| Format: | Preprint |
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2021
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| _version_ | 1866910552914132992 |
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| author | Wang, Juanyong Zhong, Guolei |
| author_facet | Wang, Juanyong Zhong, Guolei |
| contents | Let $X$ be a normal projective variety with only klt singularities, and $L_X$ a strictly nef $\mathbb{Q}$-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 sufficiently large $t\gg 1$. We show that, if $X$ is assumed to be a $\mathbb{Q}$-factorial Gorenstein terminal threefold, then $K_X+tL_X$ is ample for $t\gg 1$ unless $X$ is a weak Calabi-Yau variety (i.e., the canonical divisor $K_X\sim_\mathbb{Q}0$ and the augmented irregularity $q^\circ(X)=0$) with $L_X\cdot c_2(X)=0$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2112_03117 |
| institution | arXiv |
| publishDate | 2021 |
| record_format | arxiv |
| spellingShingle | Strictly nef divisors on singular threefolds Wang, Juanyong Zhong, Guolei Algebraic Geometry 14E30, 14J30 Let $X$ be a normal projective variety with only klt singularities, and $L_X$ a strictly nef $\mathbb{Q}$-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 sufficiently large $t\gg 1$. We show that, if $X$ is assumed to be a $\mathbb{Q}$-factorial Gorenstein terminal threefold, then $K_X+tL_X$ is ample for $t\gg 1$ unless $X$ is a weak Calabi-Yau variety (i.e., the canonical divisor $K_X\sim_\mathbb{Q}0$ and the augmented irregularity $q^\circ(X)=0$) with $L_X\cdot c_2(X)=0$. |
| title | Strictly nef divisors on singular threefolds |
| topic | Algebraic Geometry 14E30, 14J30 |
| url | https://arxiv.org/abs/2112.03117 |