Equations of linear subvarieties of strata of differentials

Abstract

For a linear subvariety $M$ of a stratum of meromorphic differentials, we investigate its closure in the multi-scale compactification constructed by Bainbridge-Chen-Gendron-Grushevsky-Möller. We prove various restrictions on the type of defining linear equations in period coordinates for $M$ near its boundary, and prove that the closure is locally a toric variety. As applications, we give a fundamentally new proof of a generalization of the cylinder deformation theorem of Wright to the case of meromorphic strata, and construct a smooth compactification of the Hurwitz space of covers of the Riemann sphere.

v2: updated version with minor edits, accepted to Geometry&Topology

References in corpus (4)

• The moduli space of multi-scale differentials
• The WYSIWYG compactification
• Measure bound for translation surfaces with short saddle connections
• Mixed Finite Element Method and numerical analysis of a convection-diffusion-reaction model in a porous medium

Cited by in corpus (1)

• Teichmüller curves in hyperelliptic components of meromorphic strata