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Teichmüller Curves Through Fermat Curves

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Abstract.

The billiard in a regular n-gon is known to give rise to a Teichmüller curve. For odd n, we compute the genus of this curve, a number field over which the curve may be defined and branched covering relations between certain pairs of these curves. If n is a power of a prime congruent to 3 or 5 modulo 8, the Teichmüller curve may be defined over the rationals.

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Authors and Affiliations

  1. Mathematics Department, MS136, Rice University, 6100 S Main St, Houston, TX, 77005, USA

    William A. Veech

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  1. William A. Veech
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Correspondence to William A. Veech.

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Received: June 2006, Revision: October 2006, Accepted: November 2006

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Veech, W.A. Teichmüller Curves Through Fermat Curves. GAFA Geom. funct. anal. 18, 1053–1085 (2008). https://doi.org/10.1007/s00039-008-0672-9

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  • DOI: https://doi.org/10.1007/s00039-008-0672-9

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