Geodesic curves on Shimura surfaces
classification
🧮 math.GT
math.GRmath.NT
keywords
commensurabilitycurvesgeodesicshimuraclassescontainssurfacestotally
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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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