Ends of the strata of differentials

Benjamin Dozier; Samuel Grushevsky; Myeongjae Lee

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arXiv · 2504.21756

Ends of the strata of differentials

Benjamin Dozier·Samuel Grushevsky·Myeongjae Lee

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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.

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Benjamin Dozier, Samuel Grushevsky, Myeongjae Lee. 2025-04-30. Ends of the strata of differentials. https://arxiv.org/abs/2504.21756

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