Differential equations associated with nonarithmetic Fuchsian groups

Abstract

We describe globally nilpotent differential operators of rank 2 defined over a number field whose monodromy group is a nonarithmetic Fuchsian group. We show that these differential operators have an S-integral solution. These differential operators are naturally associated with Teichmueller curves in genus 2. They are counterexamples to conjectures by Chudnovsky--Chudnovsky and Dwork. We also determine the field of moduli of primitive Teichmueller curves in genus 2, and an explicit equation in some cases.

Cited by in corpus (5)

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• The Ising model: from elliptic curves to modular forms and Calabi-Yau equations
• Modular embeddings of Teichmueller curves
• Algebraic models and arithmetic geometry of Teichmüller curves in genus two
• The equation of the Kenyon-Smillie $(2,3,4)$-Teichmüller curve