Seminari del Dipartimento

 

Geometria

On spherical surfaces of genus 1 with 1 conical point

Gabriele Mondello


04-02-2021 - 14:30
modalità telematica (telematic form)

 

A spherical metric on a surface is a metric of constant curvature 1, which thus makes the surface locally isometric to S^2.
Such a metric has a conical point x of angle 2pi heta if its area element vanishes of order 2( heta-1) at x.
If the conformal class is prescribed, a spherical metric can be viewed as a solution of a suitable singular Liouville equation.
If the conformal class is not prescribed, isotopy classes of spherical metrics can be considered as flat (SO(3,R),S^2)-structure, and so their deformation space has a natural finite-dimensional real-analytic structure.
Additionally, the moduli space of spherical surfaces of genus g with n conical points comes endowed with a natural forgetful map to the moduli space of Riemann surfaces of genus g with n marked points.
I will begin by giving an overview of what is known about the topology of the moduli space of spherical surfaces and the above mentioned forgetful map.
I will then focus on the case of genus 1 with 1 conical point (joint works with Eremenko-Panov and with Eremenko-Gabrielov-Panov).

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org: Barbara Bolognese

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