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Differential Geometry Seminar
The intersection of holonomy varieties of complex projective structures on Riemann surfaces
The intersection of holonomy varieties of complex projective structures on Riemann surfaces
演讲者
Shinpei Baba
时间
2025年05月20日 14:45 至 16:30
地点
A3-4-301
线上
Zoom 815 762 8413
(BIMSA)
摘要
In this talk, we discuss the intersection of certain analytic Lagrangians in the $PSL(2, C)$-character variety of a closed surface.
A holomorphic quadratic differential on a closed Riemann surface corresponds to a complex projective structure. In addition, holomorphic quadratic differentials on a fixed Riemann surface form a complex affine vector space. Then, by the holonomy map of complex projective structures, this vector space properly maps onto a smooth analytic Lagrangian subvariety of the space of representations of the surface group into $PSL(2, C)$. In this talk, given two (marked) closed Riemann surface structures of the same topological type, we show that their corresponding subvarieties intersect in an infinite discrete set.