Lev Borisov - On equations of fake projective planes with automorphism group of order $21$

epiga:8507 - Épijournal de Géométrie Algébrique, May 30, 2023, Volume 7 - https://doi.org/10.46298/epiga.2023.8507
On equations of fake projective planes with automorphism group of order $21$Article

Authors: Lev Borisov

    We study Dolgachev elliptic surfaces with a double and a triple fiber and find explicit equations of two new pairs of fake projective plane with $21$ automorphisms, thus finishing the task of finding explicit equations of fake projective planes with this automorphism group. This includes, in particular, the fake projective plane discovered by J. Keum.


    Volume: Volume 7
    Published on: May 30, 2023
    Accepted on: April 19, 2023
    Submitted on: September 21, 2021
    Keywords: Mathematics - Algebraic Geometry,14J29

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