Vol. 9, No. 4, 2015

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

Volume 14, 1 issue

Volume 13, 10 issues

Volume 12, 10 issues

Volume 11, 10 issues

Volume 10, 10 issues

Volume 9, 10 issues

Volume 8, 10 issues

Volume 7, 10 issues

Volume 6, 8 issues

Volume 5, 8 issues

Volume 4, 8 issues

Volume 3, 8 issues

Volume 2, 8 issues

Volume 1, 4 issues

The Journal
About the Journal
Editorial Board
Editors' Interests
Submission Guidelines
Submission Form
Editorial Login
Ethics Statement
ISSN: 1944-7833 (e-only)
ISSN: 1937-0652 (print)
Author Index
To Appear
Other MSP Journals
Bounded negativity of self-intersection numbers of Shimura curves in Shimura surfaces

Martin Möller and Domingo Toledo

Vol. 9 (2015), No. 4, 897–912

Shimura curves on Shimura surfaces have been a candidate for counterexamples to the bounded negativity conjecture. We prove that they do not serve this purpose: there are only finitely many whose self-intersection number lies below a given bound.

Previously (Duke Math. J. 162:10 (2013), 1877–1894), this result was shown for compact Hilbert modular surfaces using the Bogomolov–Miyaoka–Yau inequality. Our approach uses equidistribution and works uniformly for all Shimura surfaces.

bounded negativity, Shimura curves, self-intersections, equidistribution of Shimura curves
Mathematical Subject Classification 2010
Primary: 14G35
Secondary: 14J25, 22E40, 37A99, 53C55
Received: 16 August 2014
Revised: 2 March 2015
Accepted: 7 April 2015
Published: 30 May 2015
Martin Möller
Institut für Mathematik
Goethe-Universität Frankfurt
Robert-Mayer-Strasse 6–8
D-60325 Frankfurt am Main
Domingo Toledo
Department of Mathematics
University of Utah
155 S 1400 E
Salt Lake City, UT 84112
United States