Commensurability classes of fake quadrics

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 over a number field.

Publisher

Springer Verlag

Publication Date

8-1-2019

Publication Title

Selecta Mathematics - New Series

Department

Mathematics

Document Type

Article

DOI

https://dx.doi.org/10.1007/s00029-019-0492-9

Keywords

Arithmetic quotients, General type, Surfaces, Subgroups, Formulas

Language

English

Format

text

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