The moduli space of multi-scale differentials.
By Matt Bainbridge, Dawei Chen, Q. Gendron, S. Grushevsky, M. Moller. 2019
74 citations recorded by the source corpus.
We construct a compactification of the moduli spaces of abelian differentials on Riemann surfaces with prescribed zeroes and poles. This compactification, called the moduli space of multi-scale differentials, is a complex orbifold with normal crossing boundary. Locally, our compactification can be described as the normalization of an explicit blowup of the incidence variety compactification, which was defined in [BCGGM18] as the closure of the stratum of abelian differentials in the closure of the Hodge bundle. We also define families of projectivized multi-scale differentials, which gives a proper Deligne-Mumford stack, and our compactification is the orbifold corresponding to it. Moreover, we perform a real oriented blowup of the unprojectivized moduli space of multi-scale differentials such that the $\mathrm{SL}_2(\mathbb R)$-action in the interior of the moduli space extends continuously to the boundary.
Subfields: Geometry and Topology, Mathematical Physics
View Paper: https://www.semanticscholar.org/paper/484b4bd87fe9c7aa15676168c741077a77679d00
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In Geometry and Topology
- Dawei Chen
- Don Zagier
- Martin Möller
- A. Sauvaget
- Martin Moeller
- A. Libgober
- Curtis T. McMullen
- Jeremy Lovejoy
In Mathematical Physics
- Dawei Chen
- Martin Möller
- Don Zagier
- A. Sauvaget
- Tudor Dimofte
- Martin Moeller
- A. Libgober
- Jeremy Lovejoy
Citations in the corpus
- Masur–Veech volumes and intersection theory on moduli spaces of Abelian differentials (2019, background): “This assumption was already present in [42] and can be deduced from the smooth strata compactification constructed in [7].”