Rigidity for compact hyperbolic complex manifolds
Fuente:
arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866909774385250304 |
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| author | Li, Mu-Lin Rao, Sheng Wang, Mengjiao |
| author_facet | Li, Mu-Lin Rao, Sheng Wang, Mengjiao |
| contents | We study the deformation behavior of compact hyperbolic complex manifolds. Let $π:\mathcal{X}\rightarrow Δ$ be a smooth family of compact complex manifolds over the unit disk in $\mathbb{C}$, and $H$ a compact hyperbolic complex manifold. Then the $H$-locus $\{t\inΔ: X_t\cong H\}$ is either at most a discrete subset of $Δ$ or the whole $Δ$. For a smooth family over a compact Riemann surface $Y$, its $H$-locus is either at most finite or the whole $Y$. Furthermore, if $Y$ is isomorphic to $\mathbb{P}^1$ or an elliptic curve, then we conjecture that the $H$-locus is empty or the whole $Y$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2509_05707 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Rigidity for compact hyperbolic complex manifolds Li, Mu-Lin Rao, Sheng Wang, Mengjiao Complex Variables Algebraic Geometry Differential Geometry Primary 32Q45, Secondary 32G05, 14D22, 53C24, 32G13 We study the deformation behavior of compact hyperbolic complex manifolds. Let $π:\mathcal{X}\rightarrow Δ$ be a smooth family of compact complex manifolds over the unit disk in $\mathbb{C}$, and $H$ a compact hyperbolic complex manifold. Then the $H$-locus $\{t\inΔ: X_t\cong H\}$ is either at most a discrete subset of $Δ$ or the whole $Δ$. For a smooth family over a compact Riemann surface $Y$, its $H$-locus is either at most finite or the whole $Y$. Furthermore, if $Y$ is isomorphic to $\mathbb{P}^1$ or an elliptic curve, then we conjecture that the $H$-locus is empty or the whole $Y$. |
| title | Rigidity for compact hyperbolic complex manifolds |
| topic | Complex Variables Algebraic Geometry Differential Geometry Primary 32Q45, Secondary 32G05, 14D22, 53C24, 32G13 |
| url | https://arxiv.org/abs/2509.05707 |