Bounded negativity of self-intersection numbers of Shimura curves on Shimura surfaces
Algebraic Geometry
2016-01-20 v1
Abstract
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.
Keywords
Cite
@article{arxiv.1407.5181,
title = {Bounded negativity of self-intersection numbers of Shimura curves on Shimura surfaces},
author = {Martin Moeller and Domingo Toledo},
journal= {arXiv preprint arXiv:1407.5181},
year = {2016}
}
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12 pages