A boundedness theorem for principal bundles on curves
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arXiv
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| Main Authors: | , , , , |
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| Format: | Preprint |
| Published: |
2023
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| _version_ | 1866915779276963840 |
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| author | Chang, Huai-Liang Guo, Shuai Li, Jun Li, Wei-Ping Zhou, Yang |
| author_facet | Chang, Huai-Liang Guo, Shuai Li, Jun Li, Wei-Ping Zhou, Yang |
| contents | Let $G$ be a reductive group acting on an affine scheme $V$. We study the set of principal $G$-bundles on a smooth projective curve $\mathcal C$ such that the associated $V$-bundle admits a section sending the generic point of $\mathcal C$ into the GIT stable locus $V^{\mathrm{s}}(θ)$. We show that after fixing the degree of the line bundle induced by the character $θ$, the set of such principal $G$-bundles is bounded. The statement of our theorem is made slightly more general so that we deduce from it the boundedness for $ε$-stable quasimaps and $Ω$-stable LG-quasimap. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2312_11197 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | A boundedness theorem for principal bundles on curves Chang, Huai-Liang Guo, Shuai Li, Jun Li, Wei-Ping Zhou, Yang Algebraic Geometry 14H60 (Primary) 14N35, 14L17, 14L30 (Secondary) Let $G$ be a reductive group acting on an affine scheme $V$. We study the set of principal $G$-bundles on a smooth projective curve $\mathcal C$ such that the associated $V$-bundle admits a section sending the generic point of $\mathcal C$ into the GIT stable locus $V^{\mathrm{s}}(θ)$. We show that after fixing the degree of the line bundle induced by the character $θ$, the set of such principal $G$-bundles is bounded. The statement of our theorem is made slightly more general so that we deduce from it the boundedness for $ε$-stable quasimaps and $Ω$-stable LG-quasimap. |
| title | A boundedness theorem for principal bundles on curves |
| topic | Algebraic Geometry 14H60 (Primary) 14N35, 14L17, 14L30 (Secondary) |
| url | https://arxiv.org/abs/2312.11197 |