Forschungsseminar: Komplexe Geometrie
21.05.2012 Tom Sutherland (Oxford)
Painlevé cluster varieties and cubic surface
Abstract:
I will show how to construct a quiver with potential from a generic meromorphic quadratic differential on a Riemann surface. For fixed orders of the poles of the quadratic differential, these quivers with potential are mutation equivalent. For certain pole orders on the Riemann sphere given by the Painlevé equations, we will see that the corresponding cluster X-varieties of Fock and Goncharov are related to families of cubic surfaces.
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