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arXiv · 2011.11664

Equations of linear subvarieties of strata of differentials

Frederik Benirschke·Benjamin Dozier·Samuel Grushevsky
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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-M\"oller. 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.

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Frederik Benirschke, Benjamin Dozier, Samuel Grushevsky. 2020-11-23. Equations of linear subvarieties of strata of differentials. https://doi.org/10.2140/gt.2022.26.2773

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