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

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 نشر من قبل Martin Moeller
 تاريخ النشر 2014
  مجال البحث
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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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