$\mathrm{GL}^+(2,\mathbb{R})$-orbits in Prym eigenform loci
Langue
en
Article de revue
Ce document a été publié dans
Geometry and Topology. 2016-07-04, vol. 20, n° 3, p. 1359-1426
Mathematical Sciences Publishers
Résumé en anglais
This paper is devoted to the classification of GL^+(2,R)-orbit closures of surfaces in the intersection of the Prym eigenform locus with various strata of quadratic differentials. We show that the following dichotomy holds: ...Lire la suite >
This paper is devoted to the classification of GL^+(2,R)-orbit closures of surfaces in the intersection of the Prym eigenform locus with various strata of quadratic differentials. We show that the following dichotomy holds: an orbit is either closed or dense in a connected component of the Prym eigenform locus. The proof uses several topological properties of Prym eigenforms, which are proved by the authors in a previous work. In particular the tools and the proof are independent of the recent results of Eskin-Mirzakhani-Mohammadi. As an application we obtain a finiteness result for the number of closed GL^+(2,R)-orbits (not necessarily primitive) in the Prym eigenform locus Prym_D(2,2) for any fixed D that is not a square.< Réduire
Mots clés en anglais
moduli space
Prym eigenform
translation surface
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