On the component group of the algebraic monodromy group of a $K3$ surface
Fuente:
arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2023
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| Acceso en línea: | |
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| _version_ | 1866929242967638016 |
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| author | Elsenhans, Andreas-Stephan Jahnel, Jörg |
| author_facet | Elsenhans, Andreas-Stephan Jahnel, Jörg |
| contents | We provide a lower bound for the number of components of the algebraic monodromy group in the situation of a $K3$ surface over a number field $k$. In the CM case, our bound is sharp. As an application, we describe, in the case of CM, the jump character \cite[Definition~2.4.6]{CEJ} entirely in terms of the endomorphism field and the geometric Picard rank. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2304_07585 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | On the component group of the algebraic monodromy group of a $K3$ surface Elsenhans, Andreas-Stephan Jahnel, Jörg Algebraic Geometry 14F20 primary, 14J28, 14F40, 14J20 secondary We provide a lower bound for the number of components of the algebraic monodromy group in the situation of a $K3$ surface over a number field $k$. In the CM case, our bound is sharp. As an application, we describe, in the case of CM, the jump character \cite[Definition~2.4.6]{CEJ} entirely in terms of the endomorphism field and the geometric Picard rank. |
| title | On the component group of the algebraic monodromy group of a $K3$ surface |
| topic | Algebraic Geometry 14F20 primary, 14J28, 14F40, 14J20 secondary |
| url | https://arxiv.org/abs/2304.07585 |