Orphan Calabi-Yau threefold with arithmetic monodromy group
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arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2022
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| _version_ | 1866929399579803648 |
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| author | Chmiel, Tymoteusz |
| author_facet | Chmiel, Tymoteusz |
| contents | We study monodromy groups of Picard-Fuchs operators of one-parameter families of Calabi-Yau threefolds without a point of Maximal Unipotent Monodromy (\emph{orphan operators}). We construct rational symplectic bases for the monodromy action for all orphan double octic Picard-Fuchs operators of order $4$. As a consequence we show that monodromy groups of all double octic orphan operators are dense in $\mathrm{Sp(4,\mathbb{Z})}$ and identify maximally unipotent elements in all of them, except one. Finally, we prove that the monodromy group of one of these orphan operators is arithmetic. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2210_02367 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Orphan Calabi-Yau threefold with arithmetic monodromy group Chmiel, Tymoteusz Algebraic Geometry 14D05 (Primary), 11F06, 14J32 (Secondary) We study monodromy groups of Picard-Fuchs operators of one-parameter families of Calabi-Yau threefolds without a point of Maximal Unipotent Monodromy (\emph{orphan operators}). We construct rational symplectic bases for the monodromy action for all orphan double octic Picard-Fuchs operators of order $4$. As a consequence we show that monodromy groups of all double octic orphan operators are dense in $\mathrm{Sp(4,\mathbb{Z})}$ and identify maximally unipotent elements in all of them, except one. Finally, we prove that the monodromy group of one of these orphan operators is arithmetic. |
| title | Orphan Calabi-Yau threefold with arithmetic monodromy group |
| topic | Algebraic Geometry 14D05 (Primary), 11F06, 14J32 (Secondary) |
| url | https://arxiv.org/abs/2210.02367 |