Bounded negativity of self-intersection numbers of Shimura curves on Shimura surfaces

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, this result has been shown in [BHK+13] fo...

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Bibliographic Details
Published in:arXiv.org 2014-07
Main Authors: Moeller, Martin, Toledo, Domingo
Format: Article
Language:English
Subjects:
Intersections
Online Access:Get full text
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Summary: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, this result has been shown in [BHK+13] for compact Hilbert modular surfaces using the Bogomolov-Miyaoka-Yau inequality. Our approach uses equidistribution and works uniformly for all Shimura surfaces.
ISSN:2331-8422
DOI:10.48550/arxiv.1407.5181