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arXiv · 2207.04091

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

Francisco Arana-Herrera
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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.

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Francisco Arana-Herrera. 2022-07-08. Effective count of square-tiled surfaces with prescribed real and imaginary foliations in connected components of strata. https://doi.org/10.1017/etds.2024.54

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