Compactification of strata of Abelian differentials
By Matt Bainbridge, Dawei Chen, Q. Gendron, S. Grushevsky, Martin Moeller. Duke mathematical journal, 2016
130 citations recorded by the source corpus.
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.
Subfields: Applied Mathematics, Geometry and Topology
View Paper: https://www.semanticscholar.org/paper/f98e36f0776368c25c11c4315341b7e506f61f64
How researchers see this paper
The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.
In Applied Mathematics
In Geometry and Topology
- Dawei Chen
- Don Zagier
- Martin Möller
- A. Sauvaget
- Martin Moeller
- A. Libgober
- Curtis T. McMullen
- Jeremy Lovejoy
Citations in the corpus
- Masur–Veech volumes and intersection theory on moduli spaces of Abelian differentials (2019, methodology): “As in [6] we define a level graph to be a stable graph together with a level function : V ( ) → R≤0.”
- admcycles - a Sage package for calculations in the tautological ring of the moduli space of stable curves (2020, unknown): “Elements appearing in the boundary have been classified in [Bainbridge et al. 2018; 2019b] and a smooth, modular compactification has been constructed in [Bainbridge et al. 2019a].”