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 |
| _version_ | 1798029673830023168 |
|---|---|
| author | Yoshinori Hashimoto Julien Keller |
| author_facet | Yoshinori Hashimoto Julien Keller |
| author_sort | Yoshinori Hashimoto |
| collection | DOAJ |
| description | 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. |
| first_indexed | 2024-04-11T19:28:58Z |
| format | Article |
| id | doaj.art-cf4ace6aef72405e98b8d28fd0aeb716 |
| institution | Directory Open Access Journal |
| issn | 2491-6765 |
| language | English |
| last_indexed | 2024-04-11T19:28:58Z |
| publishDate | 2022-01-01 |
| publisher | Association Epiga |
| record_format | Article |
| series | Épijournal de Géométrie Algébrique |
| spelling | doaj.art-cf4ace6aef72405e98b8d28fd0aeb7162022-12-22T04:07:04ZengAssociation EpigaÉpijournal de Géométrie Algébrique2491-67652022-01-01Volume 510.46298/epiga.2022.65776577Quot-scheme limit of Fubini-Study metrics and Donaldson's functional for vector bundlesYoshinori HashimotoJulien KellerFor 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.https://epiga.episciences.org/6577/pdfmathematics - algebraic geometrymathematics - complex variablesmathematics - differential geometry14j60 (primary) 14l24, 53c07 (secondary) |
| spellingShingle | Yoshinori Hashimoto Julien Keller Quot-scheme limit of Fubini-Study metrics and Donaldson's functional for vector bundles Épijournal de Géométrie Algébrique mathematics - algebraic geometry mathematics - complex variables mathematics - differential geometry 14j60 (primary) 14l24, 53c07 (secondary) |
| title | Quot-scheme limit of Fubini-Study metrics and Donaldson's functional for vector bundles |
| title_full | Quot-scheme limit of Fubini-Study metrics and Donaldson's functional for vector bundles |
| title_fullStr | Quot-scheme limit of Fubini-Study metrics and Donaldson's functional for vector bundles |
| title_full_unstemmed | Quot-scheme limit of Fubini-Study metrics and Donaldson's functional for vector bundles |
| title_short | Quot-scheme limit of Fubini-Study metrics and Donaldson's functional for vector bundles |
| title_sort | quot scheme limit of fubini study metrics and donaldson s functional for vector bundles |
| topic | mathematics - algebraic geometry mathematics - complex variables mathematics - differential geometry 14j60 (primary) 14l24, 53c07 (secondary) |
| url | https://epiga.episciences.org/6577/pdf |
| work_keys_str_mv | AT yoshinorihashimoto quotschemelimitoffubinistudymetricsanddonaldsonsfunctionalforvectorbundles AT julienkeller quotschemelimitoffubinistudymetricsanddonaldsonsfunctionalforvectorbundles |