Compactification of strata of abelian differentials

Matt Bainbridge Department of Mathematics, Indiana University, Bloomington IN 47405 Dawei Chen Department of Mathematics, Boston College, Chestnut Hill MA 02167 Quentin Gendron Centro de Ciencias Matemáticas, National Autonomous University of Mexico (UNAM), Unidad Morelia, 58089 Morelia (Mich.), MEXICO Samuel Grushevsky Department of Mathematics, SUNY Stony Brook University, Stony Brook NY 11790 Martin Möller Mathematical Institute, Johann Wolfgang Goethe-Universität Frankfurt, D-60054 Frankfurt am Main, GERMANY

Algebraic Geometry mathscidoc:2203.45009

Duke Mathematical Journal, 167, (12), 2347-2416, 2018.8
We describe the closure of the strata of Abelian differentials with prescribed 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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  title={Compactification of strata of abelian differentials},
  author={Matt Bainbridge, Dawei Chen, Quentin Gendron, Samuel Grushevsky, and Martin Möller},
  booktitle={Duke Mathematical Journal},
Matt Bainbridge, Dawei Chen, Quentin Gendron, Samuel Grushevsky, and Martin Möller. Compactification of strata of abelian differentials. 2018. Vol. 167. In Duke Mathematical Journal. pp.2347-2416.
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