On the intersection cohomology of the moduli of $\mathrm{SL}_n$-Higgs bundles on a curve
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arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2021
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| _version_ | 1866913871306948608 |
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| author | Maulik, Davesh Shen, Junliang |
| author_facet | Maulik, Davesh Shen, Junliang |
| contents | We explore the cohomological structure for the (possibly singular) moduli of $\mathrm{SL}_n$-Higgs bundles for arbitrary degree on a genus g curve with respect to an effective divisor of degree >2g-2. We prove a support theorem for the $\mathrm{SL}_n$-Hitchin fibration extending de Cataldo's support theorem in the nonsingular case, and a version of the Hausel-Thaddeus topological mirror symmetry conjecture for intersection cohomology. This implies a generalization of the Harder-Narasimhan theorem concerning semistable vector bundles for any degree.
Our main tool is an Ngô-type support inequality established recently which works for possibly singular ambient spaces and intersection cohomology complexes. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2103_01285 |
| institution | arXiv |
| publishDate | 2021 |
| record_format | arxiv |
| spellingShingle | On the intersection cohomology of the moduli of $\mathrm{SL}_n$-Higgs bundles on a curve Maulik, Davesh Shen, Junliang Algebraic Geometry We explore the cohomological structure for the (possibly singular) moduli of $\mathrm{SL}_n$-Higgs bundles for arbitrary degree on a genus g curve with respect to an effective divisor of degree >2g-2. We prove a support theorem for the $\mathrm{SL}_n$-Hitchin fibration extending de Cataldo's support theorem in the nonsingular case, and a version of the Hausel-Thaddeus topological mirror symmetry conjecture for intersection cohomology. This implies a generalization of the Harder-Narasimhan theorem concerning semistable vector bundles for any degree. Our main tool is an Ngô-type support inequality established recently which works for possibly singular ambient spaces and intersection cohomology complexes. |
| title | On the intersection cohomology of the moduli of $\mathrm{SL}_n$-Higgs bundles on a curve |
| topic | Algebraic Geometry |
| url | https://arxiv.org/abs/2103.01285 |