## Yoshinori Hashimoto ; Julien Keller - Quot-scheme limit of Fubini-Study metrics and Donaldson's functional for vector bundles

epiga:6577 - Épijournal de Géométrie Algébrique, January 3, 2022, Volume 5 - https://doi.org/10.46298/epiga.2022.6577
Quot-scheme limit of Fubini-Study metrics and Donaldson's functional for vector bundles

Authors: Yoshinori Hashimoto ; Julien Keller

For a holomorphic vector bundle $E$ over a polarised Kähler manifold, we establish a direct link between the slope stability of $E$ and the asymptotic behaviour of Donaldson's functional, by defining the Quot-scheme limit of Fubini-Study metrics. In particular, we provide an explicit estimate which proves that Donaldson's functional is coercive on the set of Fubini-Study metrics if $E$ is slope stable, and give a new proof of Hermitian-Einstein metrics implying slope stability.

Volume: Volume 5
Published on: January 3, 2022
Accepted on: January 3, 2022
Submitted on: June 18, 2020
Keywords: Mathematics - Algebraic Geometry,Mathematics - Complex Variables,Mathematics - Differential Geometry,14J60 (Primary) 14L24, 53C07 (Secondary)