New explicit constructions of surfaces of general type
Algebraic Geometry
2020-04-23 v2
Abstract
We discover a simple construction of a four-dimensional family of smooth surfaces of general type with , with cyclic fundamental group . We use a degeneration of the surfaces in this family to find (complicated) explicit equations of six new pairs of fake projective planes. Our methods for finding new fake projective planes involve nontrivial computer calculations which we hope will be applicable in other settings.
Cite
@article{arxiv.2004.02637,
title = {New explicit constructions of surfaces of general type},
author = {Lev Borisov and Enrico Fatighenti},
journal= {arXiv preprint arXiv:2004.02637},
year = {2020}
}
Comments
17 pages, supplementary data files available at L.B.'s home page; references added to this version