Rationally connected rational double covers of primitive Fano varieties
Épijournal de Géométrie Algébrique, Tome 4 (2020)
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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.
@article{10_46298_epiga_2020_volume4_5890,
author = {Pukhlikov, Aleksandr V.},
title = {Rationally connected rational double covers of primitive {Fano} varieties},
journal = {\'Epijournal de G\'eom\'etrie Alg\'ebrique},
publisher = {mathdoc},
volume = {4},
year = {2020},
doi = {10.46298/epiga.2020.volume4.5890},
language = {en},
url = {http://geodesic.mathdoc.fr/articles/10.46298/epiga.2020.volume4.5890/}
}
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%0 Journal Article %A Pukhlikov, Aleksandr V. %T Rationally connected rational double covers of primitive Fano varieties %J Épijournal de Géométrie Algébrique %D 2020 %V 4 %I mathdoc %U http://geodesic.mathdoc.fr/articles/10.46298/epiga.2020.volume4.5890/ %R 10.46298/epiga.2020.volume4.5890 %G en %F 10_46298_epiga_2020_volume4_5890
Pukhlikov, Aleksandr V. Rationally connected rational double covers of primitive Fano varieties. Épijournal de Géométrie Algébrique, Tome 4 (2020). doi: 10.46298/epiga.2020.volume4.5890
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