Explicit equations of the fake projective plane $(a=7,p=2,\emptyset,D_3 X_7)$

TL;DR

This paper derives explicit algebraic equations for a specific fake projective plane, expanding the set of known explicit models and using a novel approach involving a Galois cover.

Contribution

It provides the first explicit equations for the fake projective plane with parameters (a=7,p=2,∅,D_3 X_7), using a new method involving a birational model of a Galois cover.

Findings

Explicit equations for the specified fake projective plane are obtained.

The method involves constructing a birational model of a Galois cover.

The approach generalizes previous work on similar surfaces.

Abstract

We find explicit equations of the fake projective plane $(a=7,p=2,\emptyset,D_3 X_7)$, which lies in the same class as the fake projective plane $(a=7,p=2,\emptyset,D_3 2_7)$ 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.