Computing periodic points on Veech surfaces

Author(s)
Chowdhury, Zawad; Everett, Samuel; Freedman, Sam; Lee, Destine
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Abstract
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. Our algorithm serves as a new proof of the finiteness of periodic points for non-square-tiled Veech surfaces. 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.
Date issued
2023-05-22
URI
https://hdl.handle.net/1721.1/150816
Department
Massachusetts Institute of Technology. Department of Mathematics
Publisher
Springer Netherlands
Citation
Geometriae Dedicata. 2023 May 22;217(4):66
Version: Author's final manuscript
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