论文标题
在几何安德烈 - 奥特猜想上
On the geometric André-Oort conjecture for variations of Hodge structures
论文作者
论文摘要
令$ \ mathbb {v} $为光滑复杂的准标记品种$ s $上的积分霍奇结构的两极分化变化。在本文中，我们表明，非因素特殊子视界的结合$（S，\ Mathbb {v}）$是Shimura类型的带有主导期间地图的类型，是$ s $的特殊subvarieties的有限结合。这概括了先前的螺旋和ullmo arXiv的结果：数学/0404131，ullmo \ cite {ullmo07}关于非因素的分布（尤其是，特别是）特殊的shimura shimura各种环境中的特殊次等体（尤其是非常强的亚体）。霍奇结构。
Let $\mathbb{V}$ be a polarized variation of integral Hodge structure on a smooth complex quasi-projective variety $S$. In this paper, we show that the union of the non-factor special subvarieties for $(S, \mathbb{V})$, which are of Shimura type with dominant period maps, is a finite union of special subvarieties of $S$. This generalizes previous results of Clozel and Ullmo arXiv:math/0404131, Ullmo \cite{Ullmo07} on the distribution of the non-factor (in particular, strongly) special subvarieties in a Shimura variety to the non-classical setting and also answers positively the geometric part of a conjecture of Klingler on the André-Oort conjecture for variations of Hodge structures.
