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Ends of the strata of differentials

2025/04/30 by Benjamin Dozier, Samuel Grushevsky, Dozier, Benjamin +3
Mathematics · #Advanced Algebra and Geometry #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Dynamical Systems (math.DS) #FOS: Mathematics #Geometric Topology (math.GT) #Holomorphic and Operator Theory

paper · pdf · doi:10.48550/arxiv.2504.21756

openalex publication_date 2025/04/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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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