Ends of the strata of differentials

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.