English

Geodesic curves on Shimura surfaces

Geometric Topology 2015-06-11 v1 Group Theory Number Theory

Abstract

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

Keywords

Cite

@article{arxiv.1506.03299,
  title  = {Geodesic curves on Shimura surfaces},
  author = {Ted Chinburg and Matthew Stover},
  journal= {arXiv preprint arXiv:1506.03299},
  year   = {2015}
}

Comments

This is broken off from our previous work arxiv:1105.1154

R2 v1 2026-06-22T09:51:00.083Z