Effective count of square-tiled surfaces with prescribed real and imaginary foliations in connected components of strata

Abstract

We prove an effective estimate with a power saving error term for the number of square-tiled surfaces in a connected component of a stratum of quadratic differentials whose vertical and horizontal foliations belong to prescribed mapping class group orbits and which have at most $L$ squares. This result strengthens asymptotic counting formulas in work of Delecroix, Goujard, Zograf, Zorich, and the author.

13 pages, 5 figures

References in corpus (2)

• Masur-Veech volumes, frequencies of simple closed geodesics and intersection numbers of moduli spaces of curves
• Effective mapping class group dynamics II: Geometric intersection numbers

Cited by in corpus (1)

• The distribution of critical graphs of Jenkins-Strebel differentials