Semi-stable quiver bundles over Gauduchon manifolds

Dan-Ni Chen; Jing Cheng; Xiao Shen; Pan Zhang; Dan-Ni Chen; Jing Cheng; Xiao Shen; Pan Zhang

doi:10.3934/math.2023584

AIMS Mathematics

2023, Volume 8, Issue 5: 11546-11556. doi: 10.3934/math.2023584

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Semi-stable quiver bundles over Gauduchon manifolds

School of Mathematical Sciences, Anhui University, Hefei 230601, China

Received: 21 December 2022 Revised: 06 March 2023 Accepted: 09 March 2023 Published: 15 March 2023
MSC : 53C07, 53C25

In this paper, we prove the existence of the approximate $ (\sigma, \tau) $-Hermitian Yang-Mills structure on the $ (\sigma, \tau) $-semi-stable quiver bundle $ \mathcal{R} = (\mathcal{E}, \phi) $ over compact Gauduchon manifolds. An interesting aspect of this work is that the argument on the weakly $ L^{2}_1 $-subbundles is different from [Álvarez-Cónsul and García-Prada, Comm. Math. Phys., 2003] and [Hu-Huang, J. Geom. Anal., 2020].
- $ (\sigma, \tau) $-semi-stability,
- approximate $ (\sigma, \tau) $-Hermitian Yang-Mills structure,
- continuity method
Citation: Dan-Ni Chen, Jing Cheng, Xiao Shen, Pan Zhang. Semi-stable quiver bundles over Gauduchon manifolds[J]. AIMS Mathematics, 2023, 8(5): 11546-11556. doi: 10.3934/math.2023584

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Abstract

In this paper, we prove the existence of the approximate $ (\sigma, \tau) $-Hermitian Yang-Mills structure on the $ (\sigma, \tau) $-semi-stable quiver bundle $ \mathcal{R} = (\mathcal{E}, \phi) $ over compact Gauduchon manifolds. An interesting aspect of this work is that the argument on the weakly $ L^{2}_1 $-subbundles is different from [Álvarez-Cónsul and García-Prada, Comm. Math. Phys., 2003] and [Hu-Huang, J. Geom. Anal., 2020].

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