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| Hlavní autoři: | , , |
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| Médium: | Preprint |
| Vydáno: |
2024
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| Témata: | |
| On-line přístup: | https://arxiv.org/abs/2409.01310 |
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| _version_ | 1866929483385143296 |
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| author | Chen, Guodu Han, Jingjun Xue, Qingyuan |
| author_facet | Chen, Guodu Han, Jingjun Xue, Qingyuan |
| contents | In this paper, we study the theory of complements, introduced by Shokurov, for Calabi-Yau type varieties with the coefficient set $[0,1]$. We show that there exists a finite set of positive integers $\mathcal{N}$, such that if a threefold pair $(X/Z\ni z,B)$ has an $\mathbb{R}$-complement which is klt over a neighborhood of $z$, then it has an $n$-complement for some $n\in\mathcal{N}$. We also show the boundedness of complements for $\mathbb{R}$-complementary surface pairs. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2409_01310 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Boundedness of complements for log Calabi-Yau threefolds Chen, Guodu Han, Jingjun Xue, Qingyuan Algebraic Geometry In this paper, we study the theory of complements, introduced by Shokurov, for Calabi-Yau type varieties with the coefficient set $[0,1]$. We show that there exists a finite set of positive integers $\mathcal{N}$, such that if a threefold pair $(X/Z\ni z,B)$ has an $\mathbb{R}$-complement which is klt over a neighborhood of $z$, then it has an $n$-complement for some $n\in\mathcal{N}$. We also show the boundedness of complements for $\mathbb{R}$-complementary surface pairs. |
| title | Boundedness of complements for log Calabi-Yau threefolds |
| topic | Algebraic Geometry |
| url | https://arxiv.org/abs/2409.01310 |