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A boundedness theorem for principal bundles on curves
Authors
Huai-Liang Chang
Shuai Guo
+3Â more
Jun Li
Wei-Ping Li
Yang Zhou
Publication date
19 December 2023
Publisher
View
on
arXiv
Abstract
Let
G
G
G
be a reductive group acting on an affine scheme
V
V
V
. We study the set of principal
G
G
G
-bundles on a smooth projective curve
C
\mathcal C
C
such that the associated
V
V
V
-bundle admits a section sending the generic point of
C
\mathcal C
C
into the GIT stable locus
V
s
(
θ
)
V^{\mathrm{s}}(\theta)
V
s
(
θ
)
. We show that after fixing the degree of the line bundle induced by the character
θ
\theta
θ
, the set of such principal
G
G
G
-bundles is bounded. The statement of our theorem is made slightly more general so that we deduce from it the boundedness for
ϵ
\epsilon
ϵ
-stable quasimaps and
Ω
\Omega
Ω
-stable LG-quasimap.Comment: 16 pages, bibliography update
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oai:arXiv.org:2312.11197
Last time updated on 08/08/2024