Commentarii Mathematici Helvetici


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Volume 92, Issue 2, 2017, pp. 257–309
DOI: 10.4171/CMH/412

Published online: 2017-05-22

Cutting out arithmetic Teichmüller curves in genus two via Theta functions

André Kappes[1] and Martin Möller[2]

(1) Goethe-Universität Frankfurt, Germany
(2) Goethe-Universität Frankfurt, Germany

We compute the class of arithmetic genus two Teichmüller curves in the Picard group of pseudo-Hilbert modular surfaces, distinguished according to their torsion order and spin invariant. As an application, we compute the number of genus two square-tiled surfaces with these invariants.

The main technical tool is the computation of divisor classes of Hilbert Jacobi forms on the universal abelian surface over the pseudo-Hilbert modular surface.

Keywords: Square-tiled surface, pseudo-Hilbert modular surfaces, Jacobi forms

Kappes André, Möller Martin: Cutting out arithmetic Teichmüller curves in genus two via Theta functions. Comment. Math. Helv. 92 (2017), 257-309. doi: 10.4171/CMH/412