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

Abstract

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.

19 pages + supplemental files

References in corpus (1)

• New explicit constructions of surfaces of general type

Cited by in corpus (1)

• On the Geometry of a Fake Projective Plane with $21$ Automorphisms