A boundedness theorem for principal bundles on curves

Fuente: arXiv
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Main Authors: Chang, Huai-Liang, Guo, Shuai, Li, Jun, Li, Wei-Ping, Zhou, Yang
Format: Preprint
Published: 2023
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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