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| Format: | Preprint |
| Veröffentlicht: |
2022
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| Schlagworte: | |
| Online-Zugang: | https://arxiv.org/abs/2210.04430 |
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| _version_ | 1866929635571269632 |
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| author | Ruan, Yongbin Shu, Cheng |
| author_facet | Ruan, Yongbin Shu, Cheng |
| contents | We study the geometry of singular $\text{SL}_n$-Hitchin fibres over the elliptic locus. We show that orbifold singularities appear in the $\text{PGL}_n$-moduli space $M^{ell}(\text{PGL}_n)$ exactly when the $\text{SL}_n$ side $M^{ell}(\text{SL}_n)$ has a reducible Hitchin fibre. Our main theorem shows that the Fourier-Mukai transform of a skyscraper sheaf supported at an orbifold singularity in $M^{ell}(\text{PGL}_n)$ satisfies a version of the fractional Hecke eigenproperty, as conjectured by Frenkel and Witten. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2210_04430 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Mirror of Orbifold Singularities in the Hitchin Fibration: the case $(\text{SL}_n,\text{PGL}_n)$ Ruan, Yongbin Shu, Cheng Algebraic Geometry We study the geometry of singular $\text{SL}_n$-Hitchin fibres over the elliptic locus. We show that orbifold singularities appear in the $\text{PGL}_n$-moduli space $M^{ell}(\text{PGL}_n)$ exactly when the $\text{SL}_n$ side $M^{ell}(\text{SL}_n)$ has a reducible Hitchin fibre. Our main theorem shows that the Fourier-Mukai transform of a skyscraper sheaf supported at an orbifold singularity in $M^{ell}(\text{PGL}_n)$ satisfies a version of the fractional Hecke eigenproperty, as conjectured by Frenkel and Witten. |
| title | Mirror of Orbifold Singularities in the Hitchin Fibration: the case $(\text{SL}_n,\text{PGL}_n)$ |
| topic | Algebraic Geometry |
| url | https://arxiv.org/abs/2210.04430 |