Geodesic curves on Shimura surfaces

zbMath1414.20017arXiv1506.03299MaRDI QIDQ4642663

Matthew Stover, Ted Chinburg

Publication date: 25 May 2018

Full work available at URL: https://arxiv.org/abs/1506.03299

zbMATH Keywords

Fuchsian groupsarithmetic groupShimura surface

Mathematics Subject Classification ID

Structure of modular groups and generalizations; arithmetic groups (11F06) Fuchsian groups and their generalizations (group-theoretic aspects) (20H10) Modular and Shimura varieties (14G35)

Related Items

On finiteness of curves with high canonical degree on a surface ⋮ Parametrizing Shimura subvarieties of \({\mathrm{A}_1}\) Shimura varieties and related geometric problems ⋮ Mini-workshop: Negative curves on algebraic surfaces. Abstracts from the mini-workshop held February 23 -- March 1, 2014. ⋮ Real hyperbolic hyperplane complements in the complex hyperbolic plane ⋮ A classification of \(\mathbb{R}\)-Fuchsian subgroups of Picard modular groups

Cites Work

• Parametrizing Shimura subvarieties of \({\mathrm{A}_1}\) Shimura varieties and related geometric problems
• Fake projective planes
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• Bounded negativity of self-intersection numbers of Shimura curves in Shimura surfaces
• Commensurability classes of arithmetic Kleinian groups and their Fuchsian subgroups
• Totally geodesic spectra of arithmetic hyperbolic spaces
• A classification of $\mathbb{C}$-Fuchsian subgroups of Picard modular groups
• Finiteness of totally geodesic exceptional divisors in Hermitian locally symmetric spaces
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