Geodesic curves on Shimura surfaces

Published 10 Jun 2015 in math.GT, math.GR, and math.NT | (1506.03299v1)

Abstract: We parametrize the commensurability classes of curves on Shimura surfaces that are totally geodesic, i.e., the commensurability classes of so-called $\mathbb{C}$-Fuchsian subgroups. In particular, if a Shimura surface contains one commensurability class of totally geodesic curves, it contains infinitely many.

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