One-dimensional strata of residueless meromorphic differentials
Fuente:
arXiv
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Preprint |
| Published: |
2023
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866908376820088832 |
|---|---|
| author | Lee, Myeongjae Tahar, Guillaume |
| author_facet | Lee, Myeongjae Tahar, Guillaume |
| contents | In projectivized strata of meromorphic $1$-forms on elliptic curves with only one zero, the locus of residueless differentials is a complex curve endowed with a canonical complex projective structure. Drawing on the multi-scale compactification of strata, we provide formulas to compute the genus of these curves and the degree of their natural forgetful map to $\mathcal{M}_{1,1}$. Additionally, we distinguish two non-hyperelliptic components in the residueless locus of the exceptional stratum $\mathcal{H}_{1}(12,-3,-3,-3,-3)$ and hence complete the classification of the connected components of these loci. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2310_13128 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | One-dimensional strata of residueless meromorphic differentials Lee, Myeongjae Tahar, Guillaume Algebraic Geometry Dynamical Systems Geometric Topology In projectivized strata of meromorphic $1$-forms on elliptic curves with only one zero, the locus of residueless differentials is a complex curve endowed with a canonical complex projective structure. Drawing on the multi-scale compactification of strata, we provide formulas to compute the genus of these curves and the degree of their natural forgetful map to $\mathcal{M}_{1,1}$. Additionally, we distinguish two non-hyperelliptic components in the residueless locus of the exceptional stratum $\mathcal{H}_{1}(12,-3,-3,-3,-3)$ and hence complete the classification of the connected components of these loci. |
| title | One-dimensional strata of residueless meromorphic differentials |
| topic | Algebraic Geometry Dynamical Systems Geometric Topology |
| url | https://arxiv.org/abs/2310.13128 |