Periodic Points of Prym Eigenforms
arXiv:2210.13503 · doi:10.3934/jmd.2024004
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 Möller's classification of periodic points of Veech surfaces in the minimal stratum in genus 2.
arXiv comment26 pages, 12 figures, comments welcome
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