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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2501.01675 |
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| _version_ | 1866929657203392512 |
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| author | Fredrickson, Laura Zimet, Max |
| author_facet | Fredrickson, Laura Zimet, Max |
| contents | We construct model hyper-Kähler geometries that include and generalize the multi-Ooguri-Vafa model using the formalism of Gaitto, Moore, and Neitzke.
This is the first paper in a series of papers making rigorous Gaiotto--Moore--Neitzke's formalism for constructing hyper-Kähler metrics near semi-flat limits. In that context, this paper describes the assumptions we will make on a sequence of lattices $0 \to Γ_{f} \to \widehatΓ \to Γ\to 0$ over a complex manifold $\mathcal{B}'=\mathcal{B} - \mathcal{B}''$ near the singular locus, $\mathcal{B}''$, in order to define a smooth manifold $\mathcal{M} \to \mathcal{B}$ and hyper-Kähler model geometries on neighborhoods of points of the singular locus. In follow-up papers, we will use a modified version of Gaiotto-Moore-Neitzke's iteration scheme starting at these model geometries to produce true global hyper-Kähler metrics on $\mathcal{M}$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2501_01675 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Hyper-Kähler manifolds from Riemann-Hilbert problems I: Ooguri-Vafa-like model geometries Fredrickson, Laura Zimet, Max Differential Geometry We construct model hyper-Kähler geometries that include and generalize the multi-Ooguri-Vafa model using the formalism of Gaitto, Moore, and Neitzke. This is the first paper in a series of papers making rigorous Gaiotto--Moore--Neitzke's formalism for constructing hyper-Kähler metrics near semi-flat limits. In that context, this paper describes the assumptions we will make on a sequence of lattices $0 \to Γ_{f} \to \widehatΓ \to Γ\to 0$ over a complex manifold $\mathcal{B}'=\mathcal{B} - \mathcal{B}''$ near the singular locus, $\mathcal{B}''$, in order to define a smooth manifold $\mathcal{M} \to \mathcal{B}$ and hyper-Kähler model geometries on neighborhoods of points of the singular locus. In follow-up papers, we will use a modified version of Gaiotto-Moore-Neitzke's iteration scheme starting at these model geometries to produce true global hyper-Kähler metrics on $\mathcal{M}$. |
| title | Hyper-Kähler manifolds from Riemann-Hilbert problems I: Ooguri-Vafa-like model geometries |
| topic | Differential Geometry |
| url | https://arxiv.org/abs/2501.01675 |