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arXiv · 1504.00470

Cutting out arithmetic Teichmueller curves in genus two via Theta functions

André Kappes·Martin Moeller
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Abstract

We compute the class of arithmetic genus two Teichmueller 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.

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André Kappes, Martin Moeller. 2015-04-02. Cutting out arithmetic Teichmueller curves in genus two via Theta functions. https://arxiv.org/abs/1504.00470

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