Geodesic
On equations of fake projective planes with automorphism group of order $21$
Épijournal de Géométrie Algébrique, Tome 7 (2023)

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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.
DOI : 10.46298/epiga.2023.8507
Classification : 14J29 
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     author = {Borisov, Lev},
     title = {On equations of fake projective planes with automorphism group of order $21$},
     journal = {\'Epijournal de G\'eom\'etrie Alg\'ebrique},
     publisher = {mathdoc},
     volume = {7},
     year = {2023},
     doi = {10.46298/epiga.2023.8507},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.46298/epiga.2023.8507/}
}
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Borisov, Lev. On equations of fake projective planes with automorphism group of order $21$. Épijournal de Géométrie Algébrique, Tome 7 (2023). doi: 10.46298/epiga.2023.8507

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