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

Abstract

This is a sequel of our paper [arXiv:1809.08425] 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.