Connected components of generalized strata of meromorphic differentials with residue conditions
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arXiv
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866915265524006912 |
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| author | Lee, Myeongjae Wong, Yiu Man |
| author_facet | Lee, Myeongjae Wong, Yiu Man |
| contents | Generalized strata of meromorphic differentials are loci within the usual strata of differentials where certain sets of residues sum to zero. They naturally appear in the boundary of the multi-scale compactification of the usual strata. The classification of generalized strata is a key step towards understanding the irreducible components of the boundary strata of the multi-scale compactification. The connected components of generalized strata of residueless differentials were classified in \cite{lee2023connected}. In the present paper, we classify the connected components of generalized strata of meromorphic differentials in full generality. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2504_20165 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Connected components of generalized strata of meromorphic differentials with residue conditions Lee, Myeongjae Wong, Yiu Man Algebraic Geometry Dynamical Systems Geometric Topology Generalized strata of meromorphic differentials are loci within the usual strata of differentials where certain sets of residues sum to zero. They naturally appear in the boundary of the multi-scale compactification of the usual strata. The classification of generalized strata is a key step towards understanding the irreducible components of the boundary strata of the multi-scale compactification. The connected components of generalized strata of residueless differentials were classified in \cite{lee2023connected}. In the present paper, we classify the connected components of generalized strata of meromorphic differentials in full generality. |
| title | Connected components of generalized strata of meromorphic differentials with residue conditions |
| topic | Algebraic Geometry Dynamical Systems Geometric Topology |
| url | https://arxiv.org/abs/2504.20165 |