Quot-scheme limit of Fubini-Study metrics and Donaldson's functional for vector bundles

Abstract

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.

38 pages. Final version

References in corpus (5)

• CM Stability And The Generalized Futaki Invariant II
• Analysis of Geometric Stability
• A variational approach to the Hermitian-Einstein metrics and the Quot-scheme limit of Fubini-Study metrics
• Quantization of Hitchin's equations for Higgs Bundles I
• Variational and non-Archimedean aspects of the Yau--Tian--Donaldson conjecture