Rationally connected rational double covers of primitive Fano varieties

Pukhlikov, Aleksandr V (2020) Rationally connected rational double covers of primitive Fano varieties. Épijournal de Géométrie Algébrique, 4.

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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 rational maps $X\dashrightarrow V$ of degree 2, where $X$ is a rationally connected variety. This fact is true for many other families of primitive Fano varieties, either. It generalizes easily for rationally connected Galois rational covers with an abelian Galois group and motivates a conjecture on absolute rigidity of primitive Fano varieties.

Item Type:	Article
Additional Information:	17 pages
Uncontrolled Keywords:	14E05, 14E07
Depositing User:	Symplectic Admin
Date Deposited:	12 Feb 2021 08:21
Last Modified:	18 Jan 2023 23:00
DOI:	10.46298/epiga.2020.volume4.5890
Related URLs:	Author Publisher
URI:	https://livrepository.liverpool.ac.uk/id/eprint/3115518

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• Rationally connected rational double covers of primitive Fano varieties. (deposited 03 Nov 2020 09:25)
  • Rationally connected rational double covers of primitive Fano varieties. (deposited 12 Jan 2021 09:07)
    • Rationally connected rational double covers of primitive Fano varieties. (deposited 12 Feb 2021 08:21) [Currently Displayed]