The equation of the Kenyon-Smillie $(2,3,4)$-Teichmüller curve

Abstract

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

Final version accepted by journal. 22 pages, 4 figures

References in corpus (4)

• On groups generated by two positive multi-twists: Teichmueller curves and Lehmer's number
• Differential equations associated with nonarithmetic Fuchsian groups
• Algebraic models and arithmetic geometry of Teichmüller curves in genus two
• Weierstrass filtration on Teichmuller curves and Lyapunov exponents

Cited by in corpus (1)

• Limit Weierstrass Points on the Kenyon-Smillie Family of Plane Quartics