Dimensional reduction of stable Higgs bundle and the Doubly-Coupled Vortex Equations
Fuente:
arXiv
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866915486213603328 |
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| author | Ono, Takashi |
| author_facet | Ono, Takashi |
| contents | Let $X$ be a compact Riemann surface and $\mathbb{P}^1$ be the complex projective line. In this paper, we introduce an equation which we call the doubly-coupled vortex equation on $X$. We show that the existence of a solution of the doubly-coupled is equivalent to the existence of an $SU(2)$-invariant Hermitian-Einstein metric on certain Higgs bundles over $X\times \mathbb{P}^1$. By applying the Kobayashi-Hitchin correspondence for Higgs bundles, we further show that the existence of a solution to the doubly-coupled vortex equation is equivalent to the stability of the associated Higgs quadruplet. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2509_07489 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Dimensional reduction of stable Higgs bundle and the Doubly-Coupled Vortex Equations Ono, Takashi Differential Geometry Algebraic Geometry Let $X$ be a compact Riemann surface and $\mathbb{P}^1$ be the complex projective line. In this paper, we introduce an equation which we call the doubly-coupled vortex equation on $X$. We show that the existence of a solution of the doubly-coupled is equivalent to the existence of an $SU(2)$-invariant Hermitian-Einstein metric on certain Higgs bundles over $X\times \mathbb{P}^1$. By applying the Kobayashi-Hitchin correspondence for Higgs bundles, we further show that the existence of a solution to the doubly-coupled vortex equation is equivalent to the stability of the associated Higgs quadruplet. |
| title | Dimensional reduction of stable Higgs bundle and the Doubly-Coupled Vortex Equations |
| topic | Differential Geometry Algebraic Geometry |
| url | https://arxiv.org/abs/2509.07489 |