From $λ$-connections to $PSL_2(\mathbb{C})$-opers with apparent singularities
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866913801807331328 |
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| author | Dinh, Duong |
| author_facet | Dinh, Duong |
| contents | On a Riemann surface of genus $> 1$, we discuss how to construct opers with apparent singularities from $SL_2(\mathbb{C})$ $λ$-connections $(E, \nabla_λ)$ and sub-line bundles $L$ of $E$. This construction defines a rational map from a space which captures important data of triples $(E, L, \nabla_λ)$ to a space which parametrises the positions and residue parameters of the induced apparent singularities. We show that this is a Poisson map with respect to natural Poisson structures. The relations to wobbly bundles and Lagrangians in the moduli spaces of Higgs bundles and $λ$-connections are discussed. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2411_03244 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | From $λ$-connections to $PSL_2(\mathbb{C})$-opers with apparent singularities Dinh, Duong Differential Geometry High Energy Physics - Theory Mathematical Physics Algebraic Geometry On a Riemann surface of genus $> 1$, we discuss how to construct opers with apparent singularities from $SL_2(\mathbb{C})$ $λ$-connections $(E, \nabla_λ)$ and sub-line bundles $L$ of $E$. This construction defines a rational map from a space which captures important data of triples $(E, L, \nabla_λ)$ to a space which parametrises the positions and residue parameters of the induced apparent singularities. We show that this is a Poisson map with respect to natural Poisson structures. The relations to wobbly bundles and Lagrangians in the moduli spaces of Higgs bundles and $λ$-connections are discussed. |
| title | From $λ$-connections to $PSL_2(\mathbb{C})$-opers with apparent singularities |
| topic | Differential Geometry High Energy Physics - Theory Mathematical Physics Algebraic Geometry |
| url | https://arxiv.org/abs/2411.03244 |