论文标题
Hodge结构的Calabi-yau变化的吸引子猜想
The Attractor Conjecture for Calabi-Yau variations of Hodge structures
论文作者
论文摘要
我们研究了Hodge结构的Calabi-yau变化的吸引子。特别是，对于某些是Shimura品种的模量空间，我们证明吸引子点是CM点，因此在这些情况下证明了Moore的吸引者猜想。我们还研究了吸引子的非BPS实例，在没有遗传结构的局部对称空间上获得了特殊点，以及Shimura品种内的局部对称空间。对于后者，我们指出了与戈尔斯基泰（Goresky-Tai）研究的子空间的可能类比。最后，在最简单的情况下，我们对非BPS吸引子进行了明确的几何描述。
We study attractor points for Calabi-Yau variations of Hodge structures. In particular, for certain moduli spaces which are Shimura varieties, we prove that the attractor points are CM points, thus proving Moore's Attractor Conjecture in these cases. We also study non-BPS examples of attractors, obtaining special points on locally symmetric spaces without hermitian structures, as well as locally symmetric spaces inside Shimura varieties; for the latter we point out a possible analogy with subspaces studied by Goresky-Tai. Finally we give an explicit geometric description of non-BPS attractors in the simplest case.
