Andrea Fanelli ; Stefan Schröer - The maximal unipotent finite quotient, unusual torsion in Fano threefolds, and exceptional Enriques surfaces

epiga:6151 - Épijournal de Géométrie Algébrique, August 19, 2020, Volume 4 - https://doi.org/10.46298/epiga.2020.volume4.6151
The maximal unipotent finite quotient, unusual torsion in Fano threefolds, and exceptional Enriques surfacesArticle

Authors: Andrea Fanelli ; Stefan Schröer

    We introduce and study the maximal unipotent finite quotient for algebraic group schemes in positive characteristics. Applied to Picard schemes, this quotient encodes unusual torsion. We construct integral Fano threefolds where such unusual torsion actually appears. The existence of such threefolds is surprising, because the torsion vanishes for del Pezzo surfaces. Our construction relies on the theory of exceptional Enriques surfaces, as developed by Ekedahl and Shepherd-Barron.


    Volume: Volume 4
    Published on: August 19, 2020
    Accepted on: August 19, 2020
    Submitted on: February 24, 2020
    Keywords: Mathematics - Algebraic Geometry,14J45, 14J28, 14L15, 14C22

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