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arXiv · 2503.21285

Relative periods of abelian differentials in a prescribed stratum

Thomas Le Fils
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Abstract

We characterise the elements of $H^1(S, Z, \mathbb C)$, where $S$ is a closed surface and $Z\subset S$ is a finite set, that arise as the relative periods of an abelian differential in a given connected component of a stratum of their moduli space. This generalises a theorem obtained independently by Bainbridge, Johnson, Judge and Park and the author, and answers a question of Filip.

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Thomas Le Fils. 2025-03-27. Relative periods of abelian differentials in a prescribed stratum. https://arxiv.org/abs/2503.21285

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