Ends of the strata of differentials
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866908344044748800 |
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| author | Dozier, Benjamin Grushevsky, Samuel Lee, Myeongjae |
| author_facet | Dozier, Benjamin Grushevsky, Samuel Lee, Myeongjae |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2504_21756 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Ends of the strata of differentials Dozier, Benjamin Grushevsky, Samuel Lee, Myeongjae Geometric Topology Algebraic Geometry Dynamical Systems 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. |
| title | Ends of the strata of differentials |
| topic | Geometric Topology Algebraic Geometry Dynamical Systems |
| url | https://arxiv.org/abs/2504.21756 |