Quot-scheme limit of Fubini-Study metrics and Donaldson's functional for vector bundles
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arXiv
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| Format: | Preprint |
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2018
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| _version_ | 1866913656750473216 |
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| author | Hashimoto, Yoshinori Keller, Julien |
| author_facet | Hashimoto, Yoshinori Keller, Julien |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_1809_08425 |
| institution | arXiv |
| publishDate | 2018 |
| record_format | arxiv |
| spellingShingle | Quot-scheme limit of Fubini-Study metrics and Donaldson's functional for vector bundles Hashimoto, Yoshinori Keller, Julien Algebraic Geometry Complex Variables Differential Geometry 14J60 (Primary) 14L24, 53C07 (Secondary) 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. |
| title | Quot-scheme limit of Fubini-Study metrics and Donaldson's functional for vector bundles |
| topic | Algebraic Geometry Complex Variables Differential Geometry 14J60 (Primary) 14L24, 53C07 (Secondary) |
| url | https://arxiv.org/abs/1809.08425 |