Brauer group of moduli stacks of parabolic principal bundles over a curve
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arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2026
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| _version_ | 1866918340396580864 |
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| author | Biswas, Indranil Chakraborty, Sujoy |
| author_facet | Biswas, Indranil Chakraborty, Sujoy |
| contents | We prove that the Brauer group of the moduli stack of parabolic stable principal $\text{PGL}(r,\mathbb{C})$-bundles on a curve $X$, for a generic system of weights along an arbitrary parabolic divisor, coincides with the Brauer group of the smooth locus of the corresponding coarse moduli space of parabolic stable principal $\text{PGL}(r,\mathbb{C})$-bundles. We also show that for any simple and simply connected complex linear algebraic group $G$, the analytic and algebraic Brauer groups of the moduli stack of quasi-parabolic principal $G$-bundles on $X$ vanish. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2602_14579 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Brauer group of moduli stacks of parabolic principal bundles over a curve Biswas, Indranil Chakraborty, Sujoy Algebraic Geometry 14D20, 14D22, 14D23, 14F22, 14H60 We prove that the Brauer group of the moduli stack of parabolic stable principal $\text{PGL}(r,\mathbb{C})$-bundles on a curve $X$, for a generic system of weights along an arbitrary parabolic divisor, coincides with the Brauer group of the smooth locus of the corresponding coarse moduli space of parabolic stable principal $\text{PGL}(r,\mathbb{C})$-bundles. We also show that for any simple and simply connected complex linear algebraic group $G$, the analytic and algebraic Brauer groups of the moduli stack of quasi-parabolic principal $G$-bundles on $X$ vanish. |
| title | Brauer group of moduli stacks of parabolic principal bundles over a curve |
| topic | Algebraic Geometry 14D20, 14D22, 14D23, 14F22, 14H60 |
| url | https://arxiv.org/abs/2602.14579 |