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Compactifications of strata of differentials

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arxiv 2401.04844 v3 pith:FDIKTWVJ submitted 2024-01-09 math.GT math.AGmath.DS

Benjamin Dozier This is my paper · ORCID
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In this informal expository note, we quickly introduce and survey compactifications of strata of holomorphic 1-forms on Riemann surfaces, i.e. spaces of translation surfaces. In the last decade, several of these have been constructed, studied, and successfully applied to problems. We discuss relations between their definitions and properties, focusing on the different notions of convergence from a flat geometric perspective.

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  1. The boundary of a totally geodesic subvariety of moduli space

    math.GT 2024-12 conditional novelty 7.0 of 10

    The boundary of a totally geodesic subvariety of moduli space is itself totally geodesic in each Deligne-Mumford boundary stratum and decomposes into prime pieces with locally isometric projections.

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