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Compact multi-monopole moduli spaces on Kähler surfaces

  • Ollie Thakar
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Abstract

We consider the multi-spinor Seiberg-Witten equations on a 4-manifold in a general setting, where we allow the auxiliary bundle to be non-trivial. We show that when the metric is Kähler and the auxiliary connection is unobstructed anti-self-dual Yang-Mills, the moduli space of solutions is compact for all parameters in some open neighborhood of the given metric and auxiliary connection. We use this fact to compute a count of solutions on some examples of Kähler surfaces. These computations have a surprising purely algebro-geometric corollary which may be of independent interest.

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Cite

BibTeXRIS
BibTeX
@misc{thakar2026compact,
  title = {{Compact multi-monopole moduli spaces on Kähler surfaces}},
  author = {Ollie Thakar},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.38595},
  eprint = {2609.38595},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.38595},
}
RIS
TY  - UNPB
TI  - Compact multi-monopole moduli spaces on Kähler surfaces
AU  - Ollie Thakar
PY  - 2026
DA  - 2026/09/29
PB  - arXiv
DO  - 10.48550/arxiv.2609.38595
UR  - https://arxiv.org/abs/2609.38595
AB  - We consider the multi-spinor Seiberg-Witten equations on a 4-manifold in a general setting, where we allow the auxiliary bundle to be non-trivial. We show that when the metric is Kähler and the auxiliary connection is unobstructed anti-self-dual Yang-Mills, the moduli space of solutions is compact for all parameters in some open neighborhood of the given metric and auxiliary connection. We use this fact to compute a count of solutions on some examples of Kähler surfaces. These computations have a surprising purely algebro-geometric corollary which may be of independent interest.
ER  -