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.

• 14J60 - Vector bundles on surfaces and higher-dimensional varieties, and their moduli
• 14L24 - Geometric invariant theory
• 53C07 - Special connections and metrics on vector bundles (Hermite-Einstein, Yang-Mills)

• 1 zbMATH Open