Non-Veech surfaces in H^hyp(4) are generic
Dynamical Systems
2014-06-19 v3 Geometric Topology
Abstract
We show that every surface in H^hyp(4) is either a Veech surface or a generic surface, i.e. its GL^+(2,R)-orbit is either a closed or a dense subset of H^hyp(4) . The proof develops new techniques applicable in general to the problem of classifying orbit closures, especially in low genus. Recent results of Eskin-Mirzakhani-Mohammadi, Avila-Eskin-M\"oller, and the second author are used. Combined with work of Matheus and the second author, a corollary is that there are at most finitely many non-arithmetic Teichm\"uller curves (closed orbits of surfaces not covering the torus) in H^hyp(4).
Cite
@article{arxiv.1306.4922,
title = {Non-Veech surfaces in H^hyp(4) are generic},
author = {Duc-Manh Nguyen and Alex Wright},
journal= {arXiv preprint arXiv:1306.4922},
year = {2014}
}