Square-tiled surfaces and rigid curves on moduli spaces

Citations of this article
Mendeley users who have this article in their library.
Get full text


We study the algebro-geometric aspects of Teichmüller curves parameterizing square-tiled surfaces with two applications.(a) There exist infinitely many rigid curves on the moduli space of hyperelliptic curves. They span the same extremal ray of the cone of moving curves. Their union is a Zariski dense subset. Hence they yield infinitely many rigid curves with the same properties on the moduli space of stable n-pointed rational curves for even n.(b) The limit of slopes of Teichmüller curves and the sum of Lyapunov exponents for the Teichmüller geodesic flow determine each other, which yields information about the cone of effective divisors on the moduli space of curves. © 2011 Elsevier Inc.




Chen, D. (2011). Square-tiled surfaces and rigid curves on moduli spaces. Advances in Mathematics, 228(2), 1135–1162. https://doi.org/10.1016/j.aim.2011.06.002

Register to see more suggestions

Mendeley helps you to discover research relevant for your work.

Already have an account?

Save time finding and organizing research with Mendeley

Sign up for free