论文标题
对称空间使Torelli基因座中的Shimura品种均匀
Symmetric spaces uniformizing Shimura varieties in the Torelli locus
论文作者
论文摘要
如果是通过Siegel空间的某些完全测量的Submanifold X的自然投影图，A_G的代数亚变量Z是完全测量的。我们说X是统一Z的对称空间。在本文中，我们确定了哪些对称空间将每个低属的反述对Coleman-oort构想的构想均匀，从而获得了研究曲线的Galois覆盖物。众所周知，通过椭圆曲线的Galois覆盖物获得的反例允许在完全测量的亚Varieties中进行两次纤维。论文的第二个结果研究了这些振动与示例的统一对称空间之间的关系。
An algebraic subvariety Z of A_g is totally geodesic if it is the image via the natural projection map of some totally geodesic submanifold X of the Siegel space. We say that X is the symmetric space uniformizing Z. In this paper we determine which symmetric space uniformizes each of the low genus counterexamples to the Coleman-Oort conjecture obtained studying Galois covers of curves. It is known that the counterexamples obtained via Galois covers of elliptic curves admit two fibrations in totally geodesic subvarieties. The second result of the paper studies the relationship between these fibrations and the uniformizing symmetric space of the examples.
