Automorphisms and quotients of Calabi-Yau threefolds of type $A$
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arXiv
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| Formato: | Preprint |
| Publicado: |
2023
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| _version_ | 1866914949658312704 |
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| author | Monti, Martina |
| author_facet | Monti, Martina |
| contents | The aim of the paper is to investigate the only two families $\mathcal{F}^A_{G}$ of Calabi-Yau $3$-folds $A/G$ with $A$ an abelian $3$-fold and $G\le \text{Aut}(A)$ a finite group acting freely: one in constructed by Catanese and Demleitner and the other is presented here. We provide a complete classification of the automorphism group of $X\in \mathcal{F}^A_{G}$. Additionally, we construct and classify the quotients $X/Υ$ for any $Υ\le \text{Aut}(X)$. Specifically, for those groups $Υ$ that preserve the volume form of $X$ then $X/Υ$ admits a desingularization $Y$ which is a Calabi-Yau $3$-fold: we compute the Hodge numbers and the fundamental group of these $Y$, thereby determining all topological in-equivalent Calabi-Yau $3$-folds obtained in this way. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2308_14615 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Automorphisms and quotients of Calabi-Yau threefolds of type $A$ Monti, Martina Algebraic Geometry The aim of the paper is to investigate the only two families $\mathcal{F}^A_{G}$ of Calabi-Yau $3$-folds $A/G$ with $A$ an abelian $3$-fold and $G\le \text{Aut}(A)$ a finite group acting freely: one in constructed by Catanese and Demleitner and the other is presented here. We provide a complete classification of the automorphism group of $X\in \mathcal{F}^A_{G}$. Additionally, we construct and classify the quotients $X/Υ$ for any $Υ\le \text{Aut}(X)$. Specifically, for those groups $Υ$ that preserve the volume form of $X$ then $X/Υ$ admits a desingularization $Y$ which is a Calabi-Yau $3$-fold: we compute the Hodge numbers and the fundamental group of these $Y$, thereby determining all topological in-equivalent Calabi-Yau $3$-folds obtained in this way. |
| title | Automorphisms and quotients of Calabi-Yau threefolds of type $A$ |
| topic | Algebraic Geometry |
| url | https://arxiv.org/abs/2308.14615 |