Explicit equations of a fake projective plane
Algebraic Geometry
2020-12-16 v3
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.
Keywords
Cite
@article{arxiv.1802.06333,
title = {Explicit equations of a fake projective plane},
author = {Lev A. Borisov and JongHae Keum},
journal= {arXiv preprint arXiv:1802.06333},
year = {2020}
}
Comments
This is a full version of "Research announcement: equations of a fake projective plane", arXiv:1710.04501. Key tables and some M2 and Magma code from the paper are included in separate files for convenience