Dmitri Panov

Moduli of spherical tori with one conical point

This talk is about joint work with Alex Eremenko and Gabriele Mondello. We consider the moduli space of tori with spherical metric which has one conical point of angle 2piϑ. We find the topology of the moduli space. In particular, for ϑ∈(2m−1,2m+1), the moduli space is connected and has orbifold Euler characteristic −m^2/12. For ϑ=2m the moduli space has a natural holomorphic structure and is biholomorphic to the quotient of Poincare disk H^2/Gm for a certain subgroup Gm of SL(2,Z) of index m^2.