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<p>This is a sequel of our paper (Hashimoto in Quot-scheme limit of Fubini–Study metrics and Donaldson’s functional for bundles <a href="http://arxiv.org/abs/1809.08425v3">arXiv:1809.08425v3</a> 2018) on the Quot-scheme limit and variational properties of Donaldson’s functional, which established its coercivity for slope stable holomorphic vector bundles over smooth projective varieties. Assuming that the coercivity is uniform in a certain sense, we provide a new proof of the Donaldson–Uhlenbeck–Yau theorem, in such a way that the analysis involved in the proof is elementary except for the asymptotic expansion of the Bergman kernel.</p>

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A variational approach to the Hermitian–Einstein metrics and the Quot-scheme limit of Fubini–Study metrics

  • 期刊论文

  • 发表日期：

    2025年5月3日

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  • Yoshinori Hashimoto,
  • Julien Keller

摘要

This is a sequel of our paper (Hashimoto in Quot-scheme limit of Fubini–Study metrics and Donaldson’s functional for bundles arXiv:1809.08425v3 2018) on the Quot-scheme limit and variational properties of Donaldson’s functional, which established its coercivity for slope stable holomorphic vector bundles over smooth projective varieties. Assuming that the coercivity is uniform in a certain sense, we provide a new proof of the Donaldson–Uhlenbeck–Yau theorem, in such a way that the analysis involved in the proof is elementary except for the asymptotic expansion of the Bergman kernel.