BIMSA > 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
Organizers
Kenji Fukaya , Lynn Heller , Sebastian Heller , Kotaro Kawai
Speaker
Shinpei Baba
Time
Tuesday, May 20, 2025 2:45 PM - 4:30 PM
Venue
A3-4-301
Online
Zoom 815 762 8413 (BIMSA)
Abstract
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.