Ends of the strata of differentials
Geometric Topology
2025-05-01 v1 Algebraic Geometry
Dynamical Systems
Abstract
We enumerate the ends of each stratum of meromorphic 1-forms on Riemann surfaces with prescribed multiplicities of zeroes and poles. Our proof uses degeneration techniques based on the construction by Bainbridge-Chen-Gendron-Grushevsky-Moeller of the moduli space of multi-scale differentials, together with recent classification of connected components of generalized strata by Lee-Wong. In particular, from these results we quickly deduce the theorem for holomorphic 1-forms, originally proved by Boissy.
Keywords
Cite
@article{arxiv.2504.21756,
title = {Ends of the strata of differentials},
author = {Benjamin Dozier and Samuel Grushevsky and Myeongjae Lee},
journal= {arXiv preprint arXiv:2504.21756},
year = {2025}
}
Comments
With an appendix by Myeongjae Lee