Non-Veech surfaces in $H^{\text{hyp}}(4)$ are generic
Idioma
en
Article de revue
Este ítem está publicado en
Geometric And Functional Analysis. 2014-07-18, vol. xx, n° xx, p. 1-20
Springer Verlag
Resumen en inglés
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 ...Leer más >
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).< Leer menos
Palabras clave en inglés
translation surface
hyperelliptic component
Orígen
Importado de HalCentros de investigación