Ponente: Bertrand Deroin
Institución: Universidad de Cergy/CNRS, Francia
06/02/2024 de 12:00 a 13:00
Dónde Auditorio "Alfonso Nápoles Gándara"
I 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 (case (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.
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