报告题目：Moduli spaces as ball quotients
报 告 人：沈 洋 （南京大学）
主 持 人：刘克峰 教授(重庆理工大学数学科学中心)
The moduli space of cubic surfaces is studied by Allcock, Carlson and Toledo. By studying the compactifications of the moduli spaces and the corresponding points in the period domain, they proved the global Torelli theorem for cubic surfaces. Moreover, they showed that the moduli space of stable cubic surfaces can be realized as a ball quotient. Several years later, they also proved similar results for cubic threefolds. Recently, we give a Hodge theoretic criterion to characterize locally the moduli spaces of certain projective manifolds to be complex balls, which is a generalization of their work. This is a joint work with Professor Kefeng Liu.