The Spectral base and quotients of bounded symmetric domains
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866916108936675328 |
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| author | He, Siqi Liu, Jie Mok, Ngaiming |
| author_facet | He, Siqi Liu, Jie Mok, Ngaiming |
| contents | In this article, we explore Higgs bundles on a projective manifold $X$, focusing on their spectral bases, a concept introduced by T.Chen and B.Ngô. The spectral base is a specific closed subscheme within the space of symmetric differentials. We observe that if the spectral base vanishes, then any reductive representation $ρ: π_1(X) \to \text{GL}_r(\mathbb{C})$ is both rigid and integral. Additionally, we prove that for $X=Ω/Γ$, a quotient of a bounded symmetric domain $Ω$ of rank at least $2$ by a torsion-free cocompact irreducible lattice $Γ$, the spectral base indeed vanishes, which generalizes a result of B.Klingler. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2401_15852 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | The Spectral base and quotients of bounded symmetric domains He, Siqi Liu, Jie Mok, Ngaiming Algebraic Geometry Complex Variables 14J60, 53C35 In this article, we explore Higgs bundles on a projective manifold $X$, focusing on their spectral bases, a concept introduced by T.Chen and B.Ngô. The spectral base is a specific closed subscheme within the space of symmetric differentials. We observe that if the spectral base vanishes, then any reductive representation $ρ: π_1(X) \to \text{GL}_r(\mathbb{C})$ is both rigid and integral. Additionally, we prove that for $X=Ω/Γ$, a quotient of a bounded symmetric domain $Ω$ of rank at least $2$ by a torsion-free cocompact irreducible lattice $Γ$, the spectral base indeed vanishes, which generalizes a result of B.Klingler. |
| title | The Spectral base and quotients of bounded symmetric domains |
| topic | Algebraic Geometry Complex Variables 14J60, 53C35 |
| url | https://arxiv.org/abs/2401.15852 |