One-cusped complex hyperbolic 2-manifolds
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arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866915652332158976 |
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| author | Deraux, Martin Stover, Matthew |
| author_facet | Deraux, Martin Stover, Matthew |
| contents | This paper builds one-cusped complex hyperbolic $2$-manifolds by an explicit geometric construction. Specifically, for each odd $d \ge 1$ there is a smooth projective surface $Z_d$ with $c_1^2(Z_d) = c_2(Z_d) = 6d$ and a smooth irreducible curve $E_d$ on $Z_d$ of genus one so that $Z_d \smallsetminus E_d$ admits a finite volume uniformization by the unit ball $\mathbb{B}^2$ in $\mathbb{C}^2$. This produces one-cusped complex hyperbolic $2$-manifolds of arbitrarily large volume. As a consequence, the $3$-dimensional nilmanifold of Euler number $12d$ bounds geometrically for all odd $d \ge 1$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2409_08028 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | One-cusped complex hyperbolic 2-manifolds Deraux, Martin Stover, Matthew Geometric Topology Algebraic Geometry This paper builds one-cusped complex hyperbolic $2$-manifolds by an explicit geometric construction. Specifically, for each odd $d \ge 1$ there is a smooth projective surface $Z_d$ with $c_1^2(Z_d) = c_2(Z_d) = 6d$ and a smooth irreducible curve $E_d$ on $Z_d$ of genus one so that $Z_d \smallsetminus E_d$ admits a finite volume uniformization by the unit ball $\mathbb{B}^2$ in $\mathbb{C}^2$. This produces one-cusped complex hyperbolic $2$-manifolds of arbitrarily large volume. As a consequence, the $3$-dimensional nilmanifold of Euler number $12d$ bounds geometrically for all odd $d \ge 1$. |
| title | One-cusped complex hyperbolic 2-manifolds |
| topic | Geometric Topology Algebraic Geometry |
| url | https://arxiv.org/abs/2409.08028 |