English

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 pg(S)=q(S)=0p_g(S)=q(S)=0, KS2=3K^2_S=3 with cyclic fundamental group C14C_{14}. 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.

Keywords

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

R2 v1 2026-06-23T14:40:58.414Z