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

Lev Borisov

doi:10.46298/epiga.2023.8507

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.

Comment: 19 pages + supplemental files

https://doi.org/10.46298/epiga.2023.8507

Source: arXiv.org:2109.02070

Volume: Volume 7

Published on: May 30, 2023

Accepted on: April 19, 2023

Submitted on: September 21, 2021

Keywords: Mathematics - Algebraic Geometry, 14J29

Licence: Attribution-ShareAlike 4.0 International (CC BY-SA 4.0)