Floer-theoretic filtration on Painlevé Hitchin systems
Fuente:
arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2024
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| _version_ | 1866916737598881792 |
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| author | Szabó, Szilárd Živanović, Filip |
| author_facet | Szabó, Szilárd Živanović, Filip |
| contents | We classify equivariant $\mathbb{C}^*$-actions on moduli spaces of Higgs bundles corresponding to the Painlevé equations. Using this, we compute the Floer-theoretic filtrations on the cohomology of these spaces, introduced by Ritter and the second author in arXiv:2304.13026. We compare it with the ``$P=W$'' and the filtration obtained by multiplicities of the irreducible components of the nilpotent cone, ultimately deducing that the Floer-theoretic filtration coincides with the multiplicity filtration, for all 2-dimensional Higgs moduli. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2405_14850 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Floer-theoretic filtration on Painlevé Hitchin systems Szabó, Szilárd Živanović, Filip Algebraic Geometry Symplectic Geometry 53D40, 14H60, 14H70 We classify equivariant $\mathbb{C}^*$-actions on moduli spaces of Higgs bundles corresponding to the Painlevé equations. Using this, we compute the Floer-theoretic filtrations on the cohomology of these spaces, introduced by Ritter and the second author in arXiv:2304.13026. We compare it with the ``$P=W$'' and the filtration obtained by multiplicities of the irreducible components of the nilpotent cone, ultimately deducing that the Floer-theoretic filtration coincides with the multiplicity filtration, for all 2-dimensional Higgs moduli. |
| title | Floer-theoretic filtration on Painlevé Hitchin systems |
| topic | Algebraic Geometry Symplectic Geometry 53D40, 14H60, 14H70 |
| url | https://arxiv.org/abs/2405.14850 |