Curvature properties and Shafarevich conjecture for toroidal compactifications of ball quotients
Fuente:
arXiv
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| Autore principale: | |
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| Natura: | Preprint |
| Pubblicazione: |
2023
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| Accesso online: | |
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| _version_ | 1866917008069623808 |
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| author | Sarem, William |
| author_facet | Sarem, William |
| contents | We study toroidal compactifications of finite volume complex hyperbolic manifolds. We obtain results on the existence or nonexistence of Kähler metrics satisfying certain nonpositive curvature properties on these compactifications. Starting from quotients of complex hyperbolic space by deep enough non-uniform arithmetic lattices, we also verify the Shafarevich conjecture for their compactifications, by showing that their universal covers are Stein. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2306_07692 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Curvature properties and Shafarevich conjecture for toroidal compactifications of ball quotients Sarem, William Complex Variables Algebraic Geometry Differential Geometry Geometric Topology We study toroidal compactifications of finite volume complex hyperbolic manifolds. We obtain results on the existence or nonexistence of Kähler metrics satisfying certain nonpositive curvature properties on these compactifications. Starting from quotients of complex hyperbolic space by deep enough non-uniform arithmetic lattices, we also verify the Shafarevich conjecture for their compactifications, by showing that their universal covers are Stein. |
| title | Curvature properties and Shafarevich conjecture for toroidal compactifications of ball quotients |
| topic | Complex Variables Algebraic Geometry Differential Geometry Geometric Topology |
| url | https://arxiv.org/abs/2306.07692 |