Periodic Points of Prym Eigenforms
Geometric Topology
2025-09-22 v1 Dynamical Systems
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.
Cite
@article{arxiv.2210.13503,
title = {Periodic Points of Prym Eigenforms},
author = {Sam Freedman},
journal= {arXiv preprint arXiv:2210.13503},
year = {2025}
}
Comments
26 pages, 12 figures, comments welcome