Rationally connected rational double covers of primitive Fano varieties
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arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2019
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| _version_ | 1866909170768281600 |
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| author | Pukhlikov, Aleksandr V. |
| author_facet | Pukhlikov, Aleksandr V. |
| contents | We show that for a Zariski general hypersurface $V$ of degree $M+1$ in ${\mathbb P}^{M+1}$ for $M\geqslant 5$ there are no Galois rational covers $X\dashrightarrow V$ of degree $d\geqslant 2$ with an abelian Galois group, where $X$ is a rationally connected variety. In particular, there are no rational maps $X\dashrightarrow V$ of degree 2 with $X$ rationally connected. This fact is true for many other families of primitive Fano varieties as well and motivates a conjecture on absolute rigidity of primitive Fano varieties. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_1910_08975 |
| institution | arXiv |
| publishDate | 2019 |
| record_format | arxiv |
| spellingShingle | Rationally connected rational double covers of primitive Fano varieties Pukhlikov, Aleksandr V. Algebraic Geometry 14E05, 14E07 We show that for a Zariski general hypersurface $V$ of degree $M+1$ in ${\mathbb P}^{M+1}$ for $M\geqslant 5$ there are no Galois rational covers $X\dashrightarrow V$ of degree $d\geqslant 2$ with an abelian Galois group, where $X$ is a rationally connected variety. In particular, there are no rational maps $X\dashrightarrow V$ of degree 2 with $X$ rationally connected. This fact is true for many other families of primitive Fano varieties as well and motivates a conjecture on absolute rigidity of primitive Fano varieties. |
| title | Rationally connected rational double covers of primitive Fano varieties |
| topic | Algebraic Geometry 14E05, 14E07 |
| url | https://arxiv.org/abs/1910.08975 |