Mirror symmetry for parabolic Higgs bundles via $p$-adic integration
Fuente:
arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2023
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| _version_ | 1866909168229679104 |
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| author | Shen, Shiyu |
| author_facet | Shen, Shiyu |
| contents | Applying the technique of $p$-adic integration, we prove the topological mirror symmetry conjecture of Hausel-Thaddeus for the moduli spaces of (strongly) parabolic Higgs bundles for the structure groups $\text{SL}_n$ and $\text{PGL}_n$, building on previous work of Groechenig-Wyss-Ziegler on the non-parabolic case. We also prove the $E$-polynomial of the smooth moduli space of parabolic $\text{GL}_n$-Higgs bundles is independent of the degree of the underlying vector bundles. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2302_02817 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Mirror symmetry for parabolic Higgs bundles via $p$-adic integration Shen, Shiyu Algebraic Geometry Representation Theory Applying the technique of $p$-adic integration, we prove the topological mirror symmetry conjecture of Hausel-Thaddeus for the moduli spaces of (strongly) parabolic Higgs bundles for the structure groups $\text{SL}_n$ and $\text{PGL}_n$, building on previous work of Groechenig-Wyss-Ziegler on the non-parabolic case. We also prove the $E$-polynomial of the smooth moduli space of parabolic $\text{GL}_n$-Higgs bundles is independent of the degree of the underlying vector bundles. |
| title | Mirror symmetry for parabolic Higgs bundles via $p$-adic integration |
| topic | Algebraic Geometry Representation Theory |
| url | https://arxiv.org/abs/2302.02817 |