Compactification of strata of Abelian differentials

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2018-03-27

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Abstract

We describe the closure of the strata of abelian differentials with pre- scribed type of zeros and poles, in the projectivized Hodge bundle over the Deligne- Mumford moduli space of stable curves with marked points. We provide an explicit characterization of pointed stable differentials in the boundary of the closure, both a complex analytic proof and a flat geometric proof for smoothing the boundary differentials, and numerous examples. The main new ingredient in our description is a global residue condition arising from a full order on the dual graph of a stable curve.

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Bainbridge, Matt, et al. "Compactification of strata of Abelian differentials." Duke Math. J., vol. 167, no. 12, pp. 2347-2416, 2018-03-27, https://doi.org/10.1215/00127094-2018-0012.

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Duke Math. J.

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