Abstract
We give an algebro-geometric construction of some of the non-arithmetic ball quotients constructed by the author, Parker and Paupert. The new construction reveals a relationship between the corresponding orbifold fundamental groups and the automorphism group of the Klein quartic, and also with groups constructed by Barthel–Hirzebruch–Höfer and Couwenberg–Heckman–Looijenga.
Acknowledgements
I would like to thank Stéphane Druel for his invaluable help with some of the technical details needed in the proof, Philippe Eyssidieux for his interest in this work, and Michel Brion for pointing to precious references about the invariants of the automorphism group of the Klein quartic. I also thank the referees for various suggestions that helped improve the manuscript.
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© 2019 Walter de Gruyter GmbH, Berlin/Boston
Articles in the same Issue
- Frontmatter
- 𝒟-modules arithmétiques sur la variété de drapeaux
- Nodal length of Steklov eigenfunctions on real-analytic Riemannian surfaces
- Kazhdan projections, random walks and ergodic theorems
- Towers of GL($r$)-type of modular curves
- Donaldson–Thomas invariants versus intersection cohomology of quiver moduli
- Volterra operators on Hardy spaces of Dirichlet series
- Mean curvature flow of noncompact hypersurfaces with Type-II curvature blow-up
- Non-arithmetic lattices and the Klein quartic
- Splitting theorems for Poisson and related structures
Articles in the same Issue
- Frontmatter
- 𝒟-modules arithmétiques sur la variété de drapeaux
- Nodal length of Steklov eigenfunctions on real-analytic Riemannian surfaces
- Kazhdan projections, random walks and ergodic theorems
- Towers of GL($r$)-type of modular curves
- Donaldson–Thomas invariants versus intersection cohomology of quiver moduli
- Volterra operators on Hardy spaces of Dirichlet series
- Mean curvature flow of noncompact hypersurfaces with Type-II curvature blow-up
- Non-arithmetic lattices and the Klein quartic
- Splitting theorems for Poisson and related structures