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 |
| _version_ | 1798029637592285184 |
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| author | Aleksandr V. Pukhlikov |
| author_facet | Aleksandr V. Pukhlikov |
| author_sort | Aleksandr V. Pukhlikov |
| collection | DOAJ |
| description | 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. |
| first_indexed | 2024-04-11T19:28:29Z |
| format | Article |
| id | doaj.art-50deb7bbaf324680823f3b3c6a813ad6 |
| institution | Directory Open Access Journal |
| issn | 2491-6765 |
| language | English |
| last_indexed | 2024-04-11T19:28:29Z |
| publishDate | 2020-11-01 |
| publisher | Association Epiga |
| record_format | Article |
| series | Épijournal de Géométrie Algébrique |
| spelling | doaj.art-50deb7bbaf324680823f3b3c6a813ad62022-12-22T04:07:04ZengAssociation EpigaÉpijournal de Géométrie Algébrique2491-67652020-11-01Volume 410.46298/epiga.2020.volume4.58905890Rationally connected rational double covers of primitive Fano varietiesAleksandr V. PukhlikovWe 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.https://epiga.episciences.org/5890/pdfmathematics - algebraic geometry14e05, 14e07 |
| spellingShingle | Aleksandr V. Pukhlikov Rationally connected rational double covers of primitive Fano varieties Épijournal de Géométrie Algébrique mathematics - algebraic geometry 14e05, 14e07 |
| title | Rationally connected rational double covers of primitive Fano varieties |
| title_full | Rationally connected rational double covers of primitive Fano varieties |
| title_fullStr | Rationally connected rational double covers of primitive Fano varieties |
| title_full_unstemmed | Rationally connected rational double covers of primitive Fano varieties |
| title_short | Rationally connected rational double covers of primitive Fano varieties |
| title_sort | rationally connected rational double covers of primitive fano varieties |
| topic | mathematics - algebraic geometry 14e05, 14e07 |
| url | https://epiga.episciences.org/5890/pdf |
| work_keys_str_mv | AT aleksandrvpukhlikov rationallyconnectedrationaldoublecoversofprimitivefanovarieties |