JournalscmhVol. 92, No. 2pp. 257–309

Cutting out arithmetic Teichmüller curves in genus two via Theta functions

  • André Kappes

    Goethe-Universität Frankfurt, Germany
  • Martin Möller

    Goethe-Universität Frankfurt, Germany
Cutting out arithmetic Teichmüller curves in genus two via Theta functions cover

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Abstract

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.

Cite this article

André Kappes, Martin Möller, Cutting out arithmetic Teichmüller curves in genus two via Theta functions. Comment. Math. Helv. 92 (2017), no. 2, pp. 257–309

DOI 10.4171/CMH/412