Computing Periodic Points on Veech Surfaces
Dynamical Systems
2023-10-12 v2 Geometric Topology
Abstract
A non-square-tiled Veech surface has finitely many periodic points, i.e., points with finite orbit under the affine automorphism group. We present an algorithm that inputs a non-square-tiled Veech surface and outputs its set of periodic points. We apply our algorithm to Prym eigenforms in the minimal stratum in genus 3, proving that in low discriminant these surfaces do not have periodic points, except for the fixed points of the Prym involution.
Keywords
Cite
@article{arxiv.2112.02698,
title = {Computing Periodic Points on Veech Surfaces},
author = {Zawad Chowdhury and Samuel Everett and Sam Freedman and Destine Lee},
journal= {arXiv preprint arXiv:2112.02698},
year = {2023}
}
Comments
20 pages, 11 figures, to appear in Geometriae Dedicata