Computing periodic points on Veech surfaces
Name
10711_2023_804_ReferencePDF.pdf
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Author(s)
Chowdhury, Zawad
Everett, Samuel
Freedman, Sam
Lee, Destine
Date Issued
May 22, 2023
Publisher
Springer Netherlands
Citation
Geometriae Dedicata. 2023 May 22;217(4):66
Version
Author's final manuscript
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.
MIT Department
Massachusetts Institute of Technology. Department of Mathematics
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Article is made available in accordance with the publisher's policy and may be subject to US copyright law. Please refer to the publisher's site for terms of use.
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DOI of Published Version
https://doi.org/10.1007/s10711-023-00804-z
