The equation of the Kenyon-Smillie (2,3,4)-Teichm\"uller curve
classification
🧮 math.GT
math.AG
keywords
equationcurveteichmulleralgebraickenyon-smillieabsoluteassociated
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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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