Brauer group of moduli stack of parabolic $\textnormal{PSp}(r,\mathbb{C})$--bundles over a curve
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| Format: | Preprint |
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2025
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| _version_ | 1866916946602098688 |
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| author | Biswas, Indranil Chakraborty, Sujoy Dey, Arijit |
| author_facet | Biswas, Indranil Chakraborty, Sujoy Dey, Arijit |
| contents | Take an irreducible smooth complex projective curve $X$ of genus $g$, with $g\,\geq\, 3$. Let $r$ be an even positive integer. We prove that the Brauer group of the moduli stack of stable parabolic $\textnormal{PSp}(r,\mathbb{C})$--bundles on $X$, of full-flag parabolic data along a set of marked points on $X$, coincides with the Brauer group of the smooth locus of the corresponding coarse moduli space of stable parabolic $\textnormal{PSp}(r,\mathbb{C})$--bundles. Under certain conditions on the parabolic types, we also compute the Brauer group of the smooth locus of this coarse moduli space. Similar computations are also done for the case of partial flags. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2509_09378 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Brauer group of moduli stack of parabolic $\textnormal{PSp}(r,\mathbb{C})$--bundles over a curve Biswas, Indranil Chakraborty, Sujoy Dey, Arijit Algebraic Geometry 14D20, 14D22, 14F22, 14H60 Take an irreducible smooth complex projective curve $X$ of genus $g$, with $g\,\geq\, 3$. Let $r$ be an even positive integer. We prove that the Brauer group of the moduli stack of stable parabolic $\textnormal{PSp}(r,\mathbb{C})$--bundles on $X$, of full-flag parabolic data along a set of marked points on $X$, coincides with the Brauer group of the smooth locus of the corresponding coarse moduli space of stable parabolic $\textnormal{PSp}(r,\mathbb{C})$--bundles. Under certain conditions on the parabolic types, we also compute the Brauer group of the smooth locus of this coarse moduli space. Similar computations are also done for the case of partial flags. |
| title | Brauer group of moduli stack of parabolic $\textnormal{PSp}(r,\mathbb{C})$--bundles over a curve |
| topic | Algebraic Geometry 14D20, 14D22, 14F22, 14H60 |
| url | https://arxiv.org/abs/2509.09378 |