25 jan 2017 -- 15:00
Aula di Consiglio, Dip.Matematica, Università "La Sapienza", Roma
Abstract.
Generalizing an idea of Thurston, Veech defines homogeneous structures on several moduli spaces of flat surfaces with cone singularities. The specific case of tori provides natural (non-complete) complex hyperbolic structures of certain complex manifolds.
We provide an interpretation of the metric completion of these manifolds in terms of degenerations of the underlying flat structures. This leads to
- on one hand, a natural compactification of the associated moduli spaces of flat surfaces;
- on the other hand, a construction of complex hyperbolic cone-manifolds of finite volume, whose holonomy are in a finite number of cases an arithmetic lattice.
This is a joint work with Luc Pirio.