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arXiv · 1601.02783

The equation of the Kenyon-Smillie $(2,3,4)$-Teichm\"uller curve

Matteo Costantini·André Kappes
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Abstract

We compute the algebraic equation of the universal family over the Kenyon-Smillie $(2,3,4)$-Teichm\"uller curve and give a nice geometric description of the torsion map. Moreover, we re-prove independently that the found algebraic equation describes a Teichm\"uller curve by computing the Picard-Fuchs equation associated to the absolute cohomology bundle.

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Matteo Costantini, André Kappes. 2016-01-12. The equation of the Kenyon-Smillie $(2,3,4)$-Teichm\"uller curve. https://doi.org/10.3934/jmd.2017002

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