Rationally connected rational double covers of primitive Fano varieties
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 ratio...
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| Format: | Article |
| Language: | English |
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Association Epiga
2020-11-01
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| Series: | Épijournal de Géométrie Algébrique |
| Subjects: | |
| Online Access: | https://epiga.episciences.org/5890/pdf |
| Summary: | 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. |
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| ISSN: | 2491-6765 |