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arXiv · 2506.24084

Counting geodesics on prime-order $k$-differentials

Juliet Aygun
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Abstract

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.

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Juliet Aygun. 2025-06-30. Counting geodesics on prime-order $k$-differentials. https://arxiv.org/abs/2506.24084

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