Translator Disclaimer
1 September 2018 Compactification of strata of Abelian differentials
Matt Bainbridge, Dawei Chen, Quentin Gendron, Samuel Grushevsky, Martin Möller
Duke Math. J. 167(12): 2347-2416 (1 September 2018). DOI: 10.1215/00127094-2018-0012

Abstract

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.

Citation

Download Citation

Matt Bainbridge. Dawei Chen. Quentin Gendron. Samuel Grushevsky. Martin Möller. "Compactification of strata of Abelian differentials." Duke Math. J. 167 (12) 2347 - 2416, 1 September 2018. https://doi.org/10.1215/00127094-2018-0012

Information

Received: 23 March 2017; Revised: 12 March 2018; Published: 1 September 2018
First available in Project Euclid: 10 August 2018

zbMATH: 06966873
MathSciNet: MR3848392
Digital Object Identifier: 10.1215/00127094-2018-0012

Subjects:
Primary: 14H10
Secondary: 32G15

Rights: Copyright © 2018 Duke University Press

JOURNAL ARTICLE
70 PAGES

This article is only available to subscribers.
It is not available for individual sale.
+ SAVE TO MY LIBRARY

SHARE
Vol.167 • No. 12 • 1 September 2018
Back to Top