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

Yoshinori Hashimoto (1) , Julien Keller (2)

1 TITECH - Tokyo Institute of Technology [Tokyo]
2 I2M - Institut de Mathématiques de Marseille

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.

Mots clés: Quot scheme; vector bundles; Bergman metrics

Domaines: Géométrie algébrique [math.AG]; Variables complexes [math.CV]; Géométrie différentielle [math.DG]

Yoshinori Hashimoto, Julien Keller. A variational approach to the Hermitian-Einstein metrics and the Quot-scheme limit of Fubini-Study metrics. Épijournal de Géométrie Algébrique, In press. ⟨hal-02868966⟩