Explicit equations of a fake projective plane

TL;DR

This paper derives explicit equations for a projective model of a conjugate pair of fake projective planes, advancing the understanding of their algebraic structure through geometric analysis of automorphism quotients.

Contribution

It provides the first explicit algebraic equations for a conjugate pair of fake projective planes, based on geometric study of automorphism quotients.

Findings

Explicit equations for a fake projective plane model

Analysis of automorphism quotient geometry

Advancement in algebraic description of fake projective planes

Abstract

Fake projective planes are smooth complex surfaces of general type with Betti numbers equal to those of the usual projective plane. They come in complex conjugate pairs and have been classified as quotients of the two-dimensional ball by explicitly written arithmetic subgroups. In this paper we find equations of a projective model of a conjugate pair of fake projective planes by studying the geometry of the quotient of such surface by an order seven automorphism.