Department of Mathematics

Dr. David Torres-Teigell (Universität des Saarlandes): "Teichmüller curves and Hilbert modular surfaces"

Nov 29, 2017 from 10:15 AM to 11:45 AM

LMS 4 - Raum 312 - Diskussionsraum


Teichmüller curves are totally geodesic complex curves C inside the moduli space of Riemann surfaces. They arise as the projection of certain orbits of the action of SL(2,R) in the Teichmüller space. By results of Möller, the Jacobian of a point in C always contains a subvariety that admits real multiplication. In particular, there exists certain Prym-Torelli map that allows us to see the curve C inside a Hilbert modular variety parametrising abelian varieties with real multiplication.

In this talk we will introduce the Gothic Teichmüller curves, discovered earlier this year by McMullen-Mukamel-Wright, and describe their Prym-Torelli images inside a Hilbert modular surface. Our main objective is to cut this image out as the vanishing locus of some Hilbert modular form and use this description to calculate their Euler characteristics.


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