Non-Veech surfaces in $H^{\text{hyp}}(4)$ are generic
Langue
en
Article de revue
Ce document a été publié dans
Geometric And Functional Analysis. 2014-07-18, vol. xx, n° xx, p. 1-20
Springer Verlag
Résumé en anglais
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 ...Lire la suite >
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).< Réduire
Mots clés en anglais
translation surface
hyperelliptic component
Origine
Importé de halUnités de recherche