Full rank affine invariant submanifolds

Abstract

We show that every GL(2, R) orbit closure of translation surfaces is either a connected component of a stratum, the hyperelliptic locus, or consists entirely of surfaces whose Jacobians have extra endomorphisms. We use this result to give applications related to polygonal billiards. For example, we exhibit infinitely many rational triangles whose unfoldings have dense GL(2,R) orbit.

minor update; final version

References in corpus (3)

• Compactification of strata of abelian differentials
• On triangular billiards
• GL(2,R)-Invariant Measures in Marked Strata: Generic Marked Points, Earle-Kra for Strata, and Illumination

Cited by in corpus (8)

• Marked points on translation surfaces
• GL(2,R)-Invariant Measures in Marked Strata: Generic Marked Points, Earle-Kra for Strata, and Illumination
• The WYSIWYG compactification
• Periodic Points in Genus Two: Holomorphic Sections over Hilbert Modular Varieties, Teichmuller Dynamics, and Billiards
• Hodge and Teichmüller
• Teichmüller curves in hyperelliptic components of meromorphic strata
• Existence of closed geodesics through a regular point on translation surfaces
• Quasidiagonals in Strata of Translation Surfaces