On the degree of a modular map
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arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866916400918953984 |
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| author | Ciliberto, Ciro verra, Alessandro |
| author_facet | Ciliberto, Ciro verra, Alessandro |
| contents | Let $X$ be a general cubic hypersurface in $\mathbb P^4$. If $x\in X$ is a general point there are exactly six distinct lines in $X$ passing through $x$, that lie on the rank 3 quadric cone with vertex $x$ of lines that have intersection multiplicity at least 3 with $X$ in $x$. So there is a natural rational map $X\dasharrow \mathcal M_2$. In this paper we compute its degree to be 2074320. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2409_12542 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | On the degree of a modular map Ciliberto, Ciro verra, Alessandro Algebraic Geometry Let $X$ be a general cubic hypersurface in $\mathbb P^4$. If $x\in X$ is a general point there are exactly six distinct lines in $X$ passing through $x$, that lie on the rank 3 quadric cone with vertex $x$ of lines that have intersection multiplicity at least 3 with $X$ in $x$. So there is a natural rational map $X\dasharrow \mathcal M_2$. In this paper we compute its degree to be 2074320. |
| title | On the degree of a modular map |
| topic | Algebraic Geometry |
| url | https://arxiv.org/abs/2409.12542 |