Quot-scheme limit of Fubini-Study metrics and Donaldson's functional for vector bundles
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 est...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
Association Epiga
2022-01-01
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| Series: | Épijournal de Géométrie Algébrique |
| Subjects: | |
| Online Access: | https://epiga.episciences.org/6577/pdf |
| Summary: | 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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| ISSN: | 2491-6765 |