Finite quotients of abelian varieties with a Calabi-Yau resolution
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arXiv
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| Format: | Preprint |
| Published: |
2022
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| _version_ | 1866909424877043712 |
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| author | Gachet, Cécile |
| author_facet | Gachet, Cécile |
| contents | Let $A$ be an abelian variety, and $G \subset Aut(A)$ a finite group acting freely in codimension two. We discuss whether the singular quotient $A/G$ admits a resolution that is a Calabi-Yau manifold. While Oguiso constructed two examples in dimension $3$, we show that there are none in dimension $4$. We also classify up to isogeny the possible abelian varieties $A$ in arbitrary dimension. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2201_00619 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Finite quotients of abelian varieties with a Calabi-Yau resolution Gachet, Cécile Algebraic Geometry Group Theory Let $A$ be an abelian variety, and $G \subset Aut(A)$ a finite group acting freely in codimension two. We discuss whether the singular quotient $A/G$ admits a resolution that is a Calabi-Yau manifold. While Oguiso constructed two examples in dimension $3$, we show that there are none in dimension $4$. We also classify up to isogeny the possible abelian varieties $A$ in arbitrary dimension. |
| title | Finite quotients of abelian varieties with a Calabi-Yau resolution |
| topic | Algebraic Geometry Group Theory |
| url | https://arxiv.org/abs/2201.00619 |