Mumford vanishing for threefolds in positive characteristic
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arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2026
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| _version_ | 1866908966477365248 |
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| author | Kawakami, Tatsuro Tanaka, Hiromu |
| author_facet | Kawakami, Tatsuro Tanaka, Hiromu |
| contents | Let $X$ be a projective klt threefold in characteristic $p>5$ and let $L$ be a nef Cartier divisor on $X$. We show that $H^1(X, -L)=0$ for the following two cases: (1) $K_X$ is not big and $L$ is big; (2) $-K_X$ is nef and $L$ is of numerical dimension two. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2604_13823 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Mumford vanishing for threefolds in positive characteristic Kawakami, Tatsuro Tanaka, Hiromu Algebraic Geometry 14F17, 14E30, 14G17 Let $X$ be a projective klt threefold in characteristic $p>5$ and let $L$ be a nef Cartier divisor on $X$. We show that $H^1(X, -L)=0$ for the following two cases: (1) $K_X$ is not big and $L$ is big; (2) $-K_X$ is nef and $L$ is of numerical dimension two. |
| title | Mumford vanishing for threefolds in positive characteristic |
| topic | Algebraic Geometry 14F17, 14E30, 14G17 |
| url | https://arxiv.org/abs/2604.13823 |