Relations between indices of Calabi--Yau varieties and pairs
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arXiv
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| Format: | Preprint |
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2023
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| _version_ | 1866909608049639424 |
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| author | Masamura, Yuto |
| author_facet | Masamura, Yuto |
| contents | We show that for any smooth Calabi--Yau variety, its index can be realized as the index of a Kawamata log terminal (klt) Calabi--Yau pair of lower dimension with standard coefficients. Our approach is based on an inductive argument on the dimension using the Beauville--Bogomolov decomposition. A key step in the argument is to prove that for $n\ge3$, any positive integer $m$ satisfying $φ(m)\le 2n$ can be realized as the index of a klt Calabi--Yau pair of dimension $n-1$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2312_16077 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Relations between indices of Calabi--Yau varieties and pairs Masamura, Yuto Algebraic Geometry 14J32 (Primary) 14E30, 14E22 (Secondary) We show that for any smooth Calabi--Yau variety, its index can be realized as the index of a Kawamata log terminal (klt) Calabi--Yau pair of lower dimension with standard coefficients. Our approach is based on an inductive argument on the dimension using the Beauville--Bogomolov decomposition. A key step in the argument is to prove that for $n\ge3$, any positive integer $m$ satisfying $φ(m)\le 2n$ can be realized as the index of a klt Calabi--Yau pair of dimension $n-1$. |
| title | Relations between indices of Calabi--Yau varieties and pairs |
| topic | Algebraic Geometry 14J32 (Primary) 14E30, 14E22 (Secondary) |
| url | https://arxiv.org/abs/2312.16077 |