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