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arXiv · 2312.11197

A boundedness theorem for principal bundles on curves

Huai-Liang Chang·Shuai Guo·Jun Li·Wei-Ping Li·Yang Zhou
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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 $V^{\mathrm{s}}(θ)$. 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.

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Huai-Liang Chang, Shuai Guo, Jun Li, Wei-Ping Li, Yang Zhou. 2026-02-06. A boundedness theorem for principal bundles on curves. https://arxiv.org/abs/2312.11197

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