Non-Veech surfaces in H^hyp(4) are generic

2013/06/20 by Duc-Manh Nguyen, Nguyen, Duc-Manh, Alex Wright +1 · 1 citation
Mathematics · #Algebraic Geometry and Number Theory #Mathematical Dynamics and Fractals #Geometric and Algebraic Topology

paper · pdf · doi:10.48550/arxiv.1306.4922

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-Möller, 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 Teichmüller curves (closed orbits of surfaces not covering the torus) in H^hyp(4).

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