Cutting out arithmetic Teichmueller curves in genus two via Theta functions
Algebraic Geometry
2015-04-03 v1 Geometric Topology
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.
Keywords
Cite
@article{arxiv.1504.00470,
title = {Cutting out arithmetic Teichmueller curves in genus two via Theta functions},
author = {André Kappes and Martin Moeller},
journal= {arXiv preprint arXiv:1504.00470},
year = {2015}
}
Comments
39 pages