Differential equations associated with nonarithmetic Fuchsian groups

• Autores: Irene I. Bouw, Martin Möller
• Localización: Journal of the London Mathematical Society, ISSN 0024-6107, Vol. 81, Nº 1, 2010, págs. 65-90
• Idioma: inglés
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• Resumen

  • 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 Teichm¨uller curves in the moduli space of curves of genus 2. They are counterexamples to conjectures by Chudnovsky�Chudnovsky and Dwork. We also determine the field of moduli of primitive Teichm¨uller curves in the moduli space of curves of genus 2, and an explicit equation in some cases.