Volume 19, issue 4 (2015)

Download this article
Download this article For screen
For printing
Recent Issues

Volume 20
Issue 4, 1807–2438
Issue 3, 1257–1806
Issue 2, 629–1255
Issue 1, 1–627

Volume 19, 6 issues

Volume 18, 5 issues

Volume 17, 5 issues

Volume 16, 4 issues

Volume 15, 4 issues

Volume 14, 5 issues

Volume 13, 5 issues

Volume 12, 5 issues

Volume 11, 4 issues

Volume 10, 4 issues

Volume 9, 4 issues

Volume 8, 3 issues

Volume 7, 2 issues

Volume 6, 2 issues

Volume 5, 2 issues

Volume 4, 1 issue

Volume 3, 1 issue

Volume 2, 1 issue

Volume 1, 1 issue

The Journal
About the Journal
Editorial Board
Editorial Interests
Editorial Procedure
Submission Guidelines
Submission Page
Subscriptions
Author Index
To Appear
Contacts
ISSN (electronic): 1364-0380
ISSN (print): 1465-3060
Varieties of general type with the same Betti numbers as $\mathbb{P}^1\times \mathbb{P}^1\times\cdots\times \mathbb{P}^1$

Amir Džambić

Geometry & Topology 19 (2015) 2257–2276
Abstract

We study quotients Γn of the n–fold product of the upper half-plane by irreducible and torsion-free lattices Γ < PSL2()n with the same Betti numbers as the n–fold product (1)n of projective lines. Such varieties are called fake products of projective lines or fake (1)n. These are higher-dimensional analogs of fake quadrics. In this paper we show that the number of fake (1)n is finite (independently of n), we give examples of fake (1)4 and show that for n > 4 there are no fake (1)n of the form Γn with Γ contained in the norm-one group of a maximal order of a quaternion algebra over a real number field.

Keywords
Varieties of general type, Betti numbers, arithmetic groups, quaternion algebras
Mathematical Subject Classification 2010
Primary: 11F06, 22E40
References
Publication
Received: 31 January 2014
Revised: 4 July 2014
Accepted: 15 October 2014
Published: 29 July 2015
Proposed: Walter Neumann
Seconded: Ronald Stern, Simon Donaldson
Authors
Amir Džambić
Institut für Mathematik
Johann Wolfgang Goethe Universität
Robert-Mayer-Str. 6-8
D-60325 Frankfurt am Main
Germany