Schwarz triangle mappings and
Teichmüller curves: Abelian square-tiled surfaces
Alex Wright - Department of Mathematics, University of Chicago, 5734 S. University Avenue, Chicago, Illinois 60637, United States (email) Abstract:
We consider normal covers of $\mathbb{C}P^1$ with abelian deck group and branched
over at most four points. Families of such covers yield arithmetic
Teichmüller curves, whose period mapping may be described
geometrically in terms of Schwarz triangle mappings. These
Teichmüller curves are generated by abelian square-tiled surfaces.
Keywords: Teichmüller curve, Schwarz triangle mapping, Lyapunov exponent.
Received: May 2012; Available Online: October 2012. |