The moduli space of multi-monopoles on a Riemann surface
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866913846834233344 |
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| author | Thakar, Ollie |
| author_facet | Thakar, Ollie |
| contents | We study the moduli space of solutions to the Seiberg-Witten equations with $N$ spinors on a compact Riemann surface. These moduli spaces arise in a program to define a new enumerative invariant of 3-manifolds. They are also of independent interest in the geometry of algebraic curves, as they parameterize generalized divisors in Brill-Noether theory for higher rank vector bundles. We compute the Euler characteristic of these spaces, completing a computation initiated by Doan, and then compute their rational homology using spectral curves and techniques of Fulton and Lazarsfeld. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2505_13166 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | The moduli space of multi-monopoles on a Riemann surface Thakar, Ollie Differential Geometry Algebraic Geometry Geometric Topology 58D27 (Primary), 14H51, 32G13, 53C07 (Secondary) We study the moduli space of solutions to the Seiberg-Witten equations with $N$ spinors on a compact Riemann surface. These moduli spaces arise in a program to define a new enumerative invariant of 3-manifolds. They are also of independent interest in the geometry of algebraic curves, as they parameterize generalized divisors in Brill-Noether theory for higher rank vector bundles. We compute the Euler characteristic of these spaces, completing a computation initiated by Doan, and then compute their rational homology using spectral curves and techniques of Fulton and Lazarsfeld. |
| title | The moduli space of multi-monopoles on a Riemann surface |
| topic | Differential Geometry Algebraic Geometry Geometric Topology 58D27 (Primary), 14H51, 32G13, 53C07 (Secondary) |
| url | https://arxiv.org/abs/2505.13166 |