2014/07/19 by Martin Möller, Martin Moeller, Domingo Toledo
Mathematics · #Advanced Algebra and Geometry #Algebra over a field #Algebraic Geometry and Number Theory #Bounded function #Geometry and complex manifolds #Negativity effect #Shimura variety #Uniform boundedness #math.AG
paper · pdf · doi:10.2140/ant.2015.9.897
published as Algebra Number Theory 9 (2015) 897-912 · 12 pages
arxiv created 2014/07/19 · openalex publication_date 2015/05/30 · arxiv updated 2016/01/20 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05
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.