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arXiv · 1910.08975

Rationally connected rational double covers of primitive Fano varieties

Aleksandr V. Pukhlikov
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Abstract

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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Aleksandr V. Pukhlikov. 2019-10-20. Rationally connected rational double covers of primitive Fano varieties. https://doi.org/10.46298/epiga.2020.volume4.5890

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