Coloquio del IMUNAM - C. U. febrero 2024

“New uniformizations of some moduli spaces of curves with marked points”

Bertrand Deroin, Universidad de Cergy/CNRS, Francia

Resumen:  will report on some work in collaboration with Julien Marché, in which we constructed some compactification of the moduli spaces of curves of genus g with n marked points carrying a complex hyperbolic structure, in the cases (g,n)= (0,4),(0,5),(1,2),(1,3) and (2,1). This extends classical works of Hirzebruch (cas  e (g,n)=(0,5)), Livne (case (g,n)=(1,2)), and this gives a negative answer to a
question asked by Siu in the eighties: there exists a holomorphic submersion X-->Y between compact complex hyperbolic manifolds X,Y of
dimensions dim X>dim Y >1. These constructions are based on the analysis of some topological properties of quantum projective
representations of the mapping class group.

https://www.matem.unam.mx/actividades/coloquio/cu/actividades/new-uniformizations-of-some-moduli-spaces-of-curves-with-marked-points