Commensurability Classes of Fake Quadrics
Algebraic Geometry
2019-06-04 v2 Group Theory
Geometric Topology
Number Theory
Abstract
A fake quadric is a smooth projective surface that has the same rational cohomology as a smooth quadric surface but is not biholomorphic to one. We provide an explicit classification of all irreducible fake quadrics according to the commensurability class of their fundamental group. To accomplish this task, we develop a number of new techniques that explicitly bound the arithmetic invariants of a fake quadric and more generally of an arithmetic manifold of bounded volume arising from a form of SL_2 over a number field.
Cite
@article{arxiv.1504.04642,
title = {Commensurability Classes of Fake Quadrics},
author = {Benjamin Linowitz and Matthew Stover and John Voight},
journal= {arXiv preprint arXiv:1504.04642},
year = {2019}
}