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

被引：16

作者：

Moeller, Martin ^{[1
]}

Toledo, Domingo ^{[2
]}

机构：

[1] Goethe Univ Frankfurt, Inst Math, D-60325 Frankfurt, Germany

[2] Univ Utah, Dept Math, Salt Lake City, UT 84112 USA

来源：

ALGEBRA & NUMBER THEORY | 2015年 / 9卷 / 04期

关键词：

bounded negativity; Shimura curves; self-intersections; equidistribution of Shimura curves; UNIPOTENT FLOWS; MODULAR FORMS; EQUIDISTRIBUTION; VARIETIES; POINTS;

D O I：

10.2140/ant.2015.9.897

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

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.

引用

页码：897 / 912

页数：16

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