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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