Quot-scheme limit of Fubini-Study metrics and Donaldson's functional for
vector bundlesArticle
Authors: Yoshinori Hashimoto ; Julien Keller
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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.