General elephants for threefold extremal contractions with one-dimensional fibers: exceptional case
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2020
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| _version_ | 1866909321316532224 |
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| author | Mori, Shigefumi Prokhorov, Yuri |
| author_facet | Mori, Shigefumi Prokhorov, Yuri |
| contents | Let $(X, C)$ be a germ of a threefold $X$ with terminal singularities along a connected reduced complete curve $C$ with a contraction $f : (X, C) \to (Z, o)$ such that $C = f^{-1} (o)_{\mathrm{red}}$ and $-K_X$ is $f$-ample. Assume that each irreducible component of $C$ contains at most one point of index $>2$. We prove that a general member $D\in |{-}K_X|$ is a normal surface with Du Val singularities. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2002_10693 |
| institution | arXiv |
| publishDate | 2020 |
| record_format | arxiv |
| spellingShingle | General elephants for threefold extremal contractions with one-dimensional fibers: exceptional case Mori, Shigefumi Prokhorov, Yuri Algebraic Geometry 14E30, 14J30, 14J17 Let $(X, C)$ be a germ of a threefold $X$ with terminal singularities along a connected reduced complete curve $C$ with a contraction $f : (X, C) \to (Z, o)$ such that $C = f^{-1} (o)_{\mathrm{red}}$ and $-K_X$ is $f$-ample. Assume that each irreducible component of $C$ contains at most one point of index $>2$. We prove that a general member $D\in |{-}K_X|$ is a normal surface with Du Val singularities. |
| title | General elephants for threefold extremal contractions with one-dimensional fibers: exceptional case |
| topic | Algebraic Geometry 14E30, 14J30, 14J17 |
| url | https://arxiv.org/abs/2002.10693 |