Periodic Points of Prym Eigenforms

Sam Freedman

doi:10.3934/jmd.2024004

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arXiv · 2210.13503

Periodic Points of Prym Eigenforms

Sam Freedman

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Abstract

A point of a Veech surface is periodic if it has a finite orbit under the surface's affine automorphism group. We show that the periodic points of Prym eigenforms in the minimal strata of translation surfaces in genera 2, 3 and 4 are the fixed points of the Prym involution. This answers a question of Apisa--Wright and gives a geometric proof of M\"oller's classification of periodic points of Veech surfaces in the minimal stratum in genus 2.

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Sam Freedman. 2022-10-24. Periodic Points of Prym Eigenforms. https://doi.org/10.3934/jmd.2024004

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