Duke Mathematical Journal
- Duke Math. J.
- Volume 167, Number 12 (2018), 2347-2416.
Compactification of strata of Abelian differentials
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.
Duke Math. J., Volume 167, Number 12 (2018), 2347-2416.
Received: 23 March 2017
Revised: 12 March 2018
First available in Project Euclid: 10 August 2018
Permanent link to this document
Digital Object Identifier
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
Primary: 14H10: Families, moduli (algebraic)
Secondary: 32G15: Moduli of Riemann surfaces, Teichmüller theory [See also 14H15, 30Fxx]
Bainbridge, Matt; Chen, Dawei; Gendron, Quentin; Grushevsky, Samuel; Möller, Martin. Compactification of strata of Abelian differentials. Duke Math. J. 167 (2018), no. 12, 2347--2416. doi:10.1215/00127094-2018-0012. https://projecteuclid.org/euclid.dmj/1533866574