Equations of linear subvarieties of strata of differentials
arXiv:2011.11664 · doi:10.2140/gt.2022.26.2773
Abstract
For a linear subvariety 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 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.
arXiv commentv2: updated version with minor edits, accepted to Geometry&Topology
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