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| Format: | Preprint |
| Publié: |
2023
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| Accès en ligne: | https://arxiv.org/abs/2303.08563 |
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| _version_ | 1866917237150973952 |
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| author | Peón-Nieto, Ana |
| author_facet | Peón-Nieto, Ana |
| contents | We give a birational description of the reduced schemes underlying the irreducible components of the nilpotent cone and the $\CC^\times$-fixed point locus of length two in the moduli space of Higgs bundles. Using these results, we prove Drinfeld's conjecture for the sublocus of type $(n_0,n_1)$ fixed points. We introduce the notion of $\U(n_0,n_1)$-wobbliness (stronger than the one of wobbliness) and show that fixed point components of type $(n_0,n_1)$ are wobbly in rank higher than three, if and only if they are also $\U(n_0,n_1)$-wobbly. This yields a computable criterion to check wobbliness of fixed point components, that simplifies the existing ones. We analyse the virtual equivariant multiplicities of fixed points of type $(n_0,n_1)$ and their Euler pairings with downward flows for type $(1,\dots, 1)$ fixed points. We find that both invariants fail to fully detect all wobbly components for ordered partitions other than $(2,1)$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2303_08563 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Wobbly moduli of chains, equivariant multiplicities and $\mathrm{U}(n_0,n_1)$-Higgs bundles Peón-Nieto, Ana Algebraic Geometry 14H60, 14H70 We give a birational description of the reduced schemes underlying the irreducible components of the nilpotent cone and the $\CC^\times$-fixed point locus of length two in the moduli space of Higgs bundles. Using these results, we prove Drinfeld's conjecture for the sublocus of type $(n_0,n_1)$ fixed points. We introduce the notion of $\U(n_0,n_1)$-wobbliness (stronger than the one of wobbliness) and show that fixed point components of type $(n_0,n_1)$ are wobbly in rank higher than three, if and only if they are also $\U(n_0,n_1)$-wobbly. This yields a computable criterion to check wobbliness of fixed point components, that simplifies the existing ones. We analyse the virtual equivariant multiplicities of fixed points of type $(n_0,n_1)$ and their Euler pairings with downward flows for type $(1,\dots, 1)$ fixed points. We find that both invariants fail to fully detect all wobbly components for ordered partitions other than $(2,1)$. |
| title | Wobbly moduli of chains, equivariant multiplicities and $\mathrm{U}(n_0,n_1)$-Higgs bundles |
| topic | Algebraic Geometry 14H60, 14H70 |
| url | https://arxiv.org/abs/2303.08563 |