1. A boundedness theorem for principal bundles on curves
- Author
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Chang, Huai-Liang, Guo, Shuai, Li, Jun, Li, Wei-Ping, and Zhou, Yang
- Subjects
Mathematics - Algebraic Geometry ,14H60 (Primary) 14N35, 14L17, 14L30 (Secondary) - Abstract
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 $V^{\mathrm{s}}(\theta)$. We show that after fixing the degree of the line bundle induced by the character $\theta$, 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 $\epsilon$-stable quasimaps and $\Omega$-stable LG-quasimap., Comment: 16 pages, bibliography updated
- Published
- 2023