The moduli space of multi-monopoles on a Riemann surface

Ollie Thakar

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arXiv · 2505.13166

The moduli space of multi-monopoles on a Riemann surface

Ollie Thakar

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Abstract

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.

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Ollie Thakar. 2025-05-19. The moduli space of multi-monopoles on a Riemann surface. https://arxiv.org/abs/2505.13166

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