$\mathrm{GL}^+(2,\mathbb{R})$-orbits in Prym eigenform loci - Archive ouverte HAL Accéder directement au contenu
Article Dans Une Revue Geometry and Topology Année : 2016

$\mathrm{GL}^+(2,\mathbb{R})$-orbits in Prym eigenform loci

Erwan Lanneau

Résumé

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.

Dates et versions

hal-01258856 , version 1 (19-01-2016)

Identifiants

Citer

Erwan Lanneau, Duc-Manh Nguyen. $\mathrm{GL}^+(2,\mathbb{R})$-orbits in Prym eigenform loci. Geometry and Topology, 2016, 20 (3), pp.1359-1426. ⟨hal-01258856⟩
60 Consultations
0 Téléchargements

Altmetric

Partager

Gmail Facebook X LinkedIn More