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arXiv · 1809.08425

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

Yoshinori Hashimoto·Julien Keller
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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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BibTeXRIS

Yoshinori Hashimoto, Julien Keller. 2018-09-22. Quot-scheme limit of Fubini-Study metrics and Donaldson's functional for vector bundles. https://doi.org/10.46298/epiga.2022.6577

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