Fundamental groups of toroidal compactifications

@article{Kasparian2014FundamentalGO,
  title={Fundamental groups of toroidal compactifications},
  author={Azniv Kasparian and Gregory Sankaran},
  journal={arXiv: Algebraic Geometry},
  year={2014}
}
We compute the fundamental group of a toroidal compactification of a Hermitian locally symmetric space $D/\Gamma$, without assuming either that $\Gamma$is neat or that it is arithmetic. We also give bounds for the first Betti number. 
1 Citations
Bielliptic ball quotient compactifications and lattices in PU(2, 1) with finitely generated commutator subgroup
We construct two infinite families of ball quotient compactifications birational to bielliptic surfaces. For each family, the volume spectrum of the associated noncompact finite volume ball quotientExpand

References

SHOWING 1-10 OF 27 REFERENCES
Fundamental group of locally symmetric varieties
We investigate the fundamental group of a compactified locally symmetric variety after resolution of singularities. We show that it can be any finite group and give examples to show that even forExpand
The Fundamental Group of Some Siegel Modular Threefolds
Let A be the moduli space of (1,p)-polarised abelian surfaces with a level structure, for p an odd prime. Let X be a desingularisation of any algebraic compactification of A. Then X isExpand
Abelianisation of orthogonal groups and the fundamental group of modular varieties
Abstract We study the commutator subgroup of integral orthogonal groups belonging to indefinite quadratic forms. We show that the index of this commutator is 2 for many groups that occur in theExpand
The fundamental group of the orbit space of a discontinuous group
A group G of homeomorphisms of a topological space X will be called discontinuous if (1) the stabilizer of each point of X is finite, and (2) each point x ∈ X ; has a neighbourhood U such that anyExpand
Projective Algebraicity of Minimal Compactifications of Complex-Hyperbolic Space Forms of Finite Volume
Let Ωbe a bounded symmetric domain and Γ⊂ Aut(Ω) be an irreducible nonuniform torsion-free discrete subgroup. When Γis of rank ≥ 2, Γis necessarily arithmetic, and X :=Ω/Γ?admits a Satake-Baily-BorelExpand
Über die Fundamentalgruppen Siegelscher Modulvarietäten vom Grade 2
We show by elementary methods that IGUSAs desingularisation (and hence any desingularisation) of SATAKEs compactification of S2/Γ2(n) is simply-connected for n⩾2. Here S2 is SIEGELs upper half planeExpand
Differential Geometry, Lie Groups, and Symmetric Spaces
Elementary differential geometry Lie groups and Lie algebras Structure of semisimple Lie algebras Symmetric spaces Decomposition of symmetric spaces Symmetric spaces of the noncompact type SymmetricExpand
Introduction to toric varieties
The course given during the School and Workshop “The Geometry and Topology of Singularities”, 8-26 January 2007, Cuernavaca, Mexico is based on a previous course given during the 23o ColoquioExpand
Compactifications of Symmetric and Locally Symmetric Spaces
* Preface * Introduction Part I: Compactifications of Riemannian Symmetric Spaces * Review of Classical Compactifications of Symmetric Spaces * Uniform Construction of Compactifications of SymmetricExpand
...
1
2
3
...