The moduli space of conically singular instantons over an SU(3)-manifold
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arXiv
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| Format: | Preprint |
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2026
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| _version_ | 1866914454058303488 |
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| author | Gutwein, Dominik Wang, Yuanqi |
| author_facet | Gutwein, Dominik Wang, Yuanqi |
| contents | In this article we study the moduli space of conically singular instantons (or Hermitian Yang--Mills connections) with prescribed tangent connections over a 6-manifold equipped with an $\mathrm{SU}(3)$-structure. That is, we develop a Fredholm deformation theory for such $\mathrm{SU}(3)$-instantons in which we fix the tangent connection but allow the underlying principal bundle (and, in particular, the singular set) to vary. This leads to the existence of a Kuranishi structure for this moduli space. Moreover, we investigate the cokernel of the instanton deformation operator and give under certain assumptions a formula for its dimension. Ultimately, we apply our results to conically singular instantons with structure group $\mathbb{P}\mathrm{U}(n)$ and give a formula for the virtual dimension of their moduli space in terms of sheaf cohomology of certain vector bundles over $\mathbb{P}^2$. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2604_06057 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | The moduli space of conically singular instantons over an SU(3)-manifold Gutwein, Dominik Wang, Yuanqi Differential Geometry 53C07, 53C25, 53C38 In this article we study the moduli space of conically singular instantons (or Hermitian Yang--Mills connections) with prescribed tangent connections over a 6-manifold equipped with an $\mathrm{SU}(3)$-structure. That is, we develop a Fredholm deformation theory for such $\mathrm{SU}(3)$-instantons in which we fix the tangent connection but allow the underlying principal bundle (and, in particular, the singular set) to vary. This leads to the existence of a Kuranishi structure for this moduli space. Moreover, we investigate the cokernel of the instanton deformation operator and give under certain assumptions a formula for its dimension. Ultimately, we apply our results to conically singular instantons with structure group $\mathbb{P}\mathrm{U}(n)$ and give a formula for the virtual dimension of their moduli space in terms of sheaf cohomology of certain vector bundles over $\mathbb{P}^2$. |
| title | The moduli space of conically singular instantons over an SU(3)-manifold |
| topic | Differential Geometry 53C07, 53C25, 53C38 |
| url | https://arxiv.org/abs/2604.06057 |