Gespeichert in:
| 1. Verfasser: | |
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| Schlagworte: | |
| Online-Zugang: | https://arxiv.org/abs/2506.24084 |
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Inhaltsangabe:
- We determine weak asymptotics of counting functions on generic surfaces in a component of a stratum of $k$-differentials when $k$ is prime and genus is greater than $2$. In order to do so, we classify the $GL^+(2,\mathbb{R})$-orbit closure of holonomy covers of components and apply Eskin-Mirzakhani-Mohammadi generalized to translation surfaces. We show that the $GL^+(2,\mathbb{R})$-orbit closure of these holonomy covers is generically a component of a stratum of translation surfaces or a hyperelliptic locus therein.