Explicit equations of the fake projective plane $(a=7,p=2,\varnothing ,D_3{X}_7)$

Abstract

We find explicit equations of the fake projective plane $(a=7,p=2,\varnothing ,D_3{X}_7)$, which lies in the same class as the fake projective plane $(a=7,p=2,\varnothing ,D_3{2}_7)$ with $21$ automorphisms whose equations were previously found by Borisov and Keum. The method involves finding a birational model of a common Galois cover of these two surfaces.

12 pages. The relevant Mathematica, Magma, Macaulay2 codes and equations produced can be found in the ancillary folder and links in the bibliography