Aleksandr V. Pukhlikov - Rationally connected rational double covers of primitive Fano varieties

epiga:5890 - Épijournal de Géométrie Algébrique, 30 novembre 2020, Volume 4 - https://doi.org/10.46298/epiga.2020.volume4.5890
Rationally connected rational double covers of primitive Fano varietiesArticle

Auteurs : Aleksandr V. Pukhlikov

    We show that for a Zariski general hypersurface V of degree M+1 in PM+1 for M5 there are no Galois rational covers XV of degree d2 with an abelian Galois group, where X is a rationally connected variety. In particular, there are no rational maps XV 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.


    Volume : Volume 4
    Publié le : 30 novembre 2020
    Accepté le : 30 novembre 2020
    Soumis le : 3 novembre 2019
    Mots-clés : Mathematics - Algebraic Geometry,14E05, 14E07

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