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

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arxiv 1809.08425 v4 pith:PZHPON5W submitted 2018-09-22 math.AG math.CVmath.DG

Yoshinori Hashimoto , Julien Keller This is my paper · ORCID
classification math.AGmath.CVmath.DG
keywords metricsdonaldsonfubini-studyfunctionalslopelimitquot-schemestability
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abstract

For a holomorphic vector bundle $E$ over a polarised K\"ahler 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.

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