Compactification of strata of Abelian differentials
Compactification of strata of Abelian differentials
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DOI：
10.1215/00127094-2018-0012
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发表时间：
2016-04
影响因子：
2.5
通讯作者：
Matt Bainbridge;Dawei Chen;Q. Gendron;S. Grushevsky;Martin Moeller
中科院分区：
文献类型：
--
作者：
Matt Bainbridge;Dawei Chen;Q. Gendron;S. Grushevsky;Martin Moeller
本文描述了在Deligne-Mumford模空间上的射影Hodge丛中具有指定类型零点和极点的阿贝尔微分层的封闭性。我们提供了一个明确的特点指出稳定的微分在封闭的边界，一个复杂的分析证明和平坦的几何证明平滑的边界微分，和众多的例子。在我们的描述中的主要新成分是一个全球性的残留条件所产生的一个完整的秩序上的对偶图的稳定曲线。
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.