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Orbifold points on Prym-Teichmüller Curves in genus 3

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Speaker: 
Jonathan Zachhuber
Affiliation: 
U Frankfurf
Date: 
Thu, 2015-07-16 16:30 - 17:30
Location: 
MPIM Lecture Hall

Teichmüller curves are special curves in the moduli space M_g that
exhibit interesting arithmetic and geometric properties. We calculate
the number and types of orbifold points for a class of Teichmüller
curves inside M_3, thus completing their topological classification.
Crucial for the determination of the orbifold points is the analysis of
families of genus 3 cyclic covers of degree 4 and 6, branched over four
points of P^1. As a side product of our study, we provide an explicit
description of the Jacobians and the Prym-Torelli images of these two
families.

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