Lev A. Borisov, JongHae Keum
Published 2018-02-18Version 1
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.
Comments: This is a full version of "Research announcement: equations of a fake projective plane", arXiv:1710.04501
Explicit equations of the fake projective plane $(a=7,p=2,\emptyset,D_3 X_7)$
Explicit equations of the fake projective plane $(C20,p=2,\emptyset,D_3 2_7)$
A journey from the octonionic $\mathbb P^2$ to a fake $\mathbb P^2$
![QR code for arXiv:1802.06333 [math.AG]](http://oss.arxitics.com/images/favicon.svg)