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arXiv · 1407.5181

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

Martin Moeller·Domingo Toledo
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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.

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Martin Moeller, Domingo Toledo. 2014-07-19. Bounded negativity of self-intersection numbers of Shimura curves on Shimura surfaces. https://doi.org/10.2140/ant.2015.9.897

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