Kobayashi—Hitchin correspondence for twisted vector bundles
We prove the Kobayashi—Hitchin correspondence and the approximate Kobayashi—Hitchin correspondence for twisted holomorphic vector bundles on compact Kähler manifolds. More precisely, if X is a compact manifold and g is a Gauduchon metric on X, a twisted holomorphic vector bundle on X is g−polystable...
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De Gruyter
2021
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oai:doaj.org-article:a9b61cfbe7854a5f91c9f3fecd75a7972021-12-05T14:10:45ZKobayashi—Hitchin correspondence for twisted vector bundles2300-744310.1515/coma-2020-0107https://doaj.org/article/a9b61cfbe7854a5f91c9f3fecd75a7972021-01-01T00:00:00Zhttps://doi.org/10.1515/coma-2020-0107https://doaj.org/toc/2300-7443We prove the Kobayashi—Hitchin correspondence and the approximate Kobayashi—Hitchin correspondence for twisted holomorphic vector bundles on compact Kähler manifolds. More precisely, if X is a compact manifold and g is a Gauduchon metric on X, a twisted holomorphic vector bundle on X is g−polystable if and only if it is g−Hermite-Einstein, and if X is a compact Kähler manifold and g is a Kähler metric on X, then a twisted holomorphic vector bundle on X is g−semistable if and only if it is approximate g−Hermite-Einstein.Perego ArvidDe Gruyterarticletwisted vector bundlessemistabilityhermite-einsten metrics32l0553c0714j6053d1853c2853c1515a6632l25MathematicsQA1-939ENComplex Manifolds, Vol 8, Iss 1, Pp 1-95 (2021) |
| institution |
DOAJ |
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DOAJ |
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EN |
| topic |
twisted vector bundles semistability hermite-einsten metrics 32l05 53c07 14j60 53d18 53c28 53c15 15a66 32l25 Mathematics QA1-939 |
| spellingShingle |
twisted vector bundles semistability hermite-einsten metrics 32l05 53c07 14j60 53d18 53c28 53c15 15a66 32l25 Mathematics QA1-939 Perego Arvid Kobayashi—Hitchin correspondence for twisted vector bundles |
| description |
We prove the Kobayashi—Hitchin correspondence and the approximate Kobayashi—Hitchin correspondence for twisted holomorphic vector bundles on compact Kähler manifolds. More precisely, if X is a compact manifold and g is a Gauduchon metric on X, a twisted holomorphic vector bundle on X is g−polystable if and only if it is g−Hermite-Einstein, and if X is a compact Kähler manifold and g is a Kähler metric on X, then a twisted holomorphic vector bundle on X is g−semistable if and only if it is approximate g−Hermite-Einstein. |
| format |
article |
| author |
Perego Arvid |
| author_facet |
Perego Arvid |
| author_sort |
Perego Arvid |
| title |
Kobayashi—Hitchin correspondence for twisted vector bundles |
| title_short |
Kobayashi—Hitchin correspondence for twisted vector bundles |
| title_full |
Kobayashi—Hitchin correspondence for twisted vector bundles |
| title_fullStr |
Kobayashi—Hitchin correspondence for twisted vector bundles |
| title_full_unstemmed |
Kobayashi—Hitchin correspondence for twisted vector bundles |
| title_sort |
kobayashi—hitchin correspondence for twisted vector bundles |
| publisher |
De Gruyter |
| publishDate |
2021 |
| url |
https://doaj.org/article/a9b61cfbe7854a5f91c9f3fecd75a797 |
| work_keys_str_mv |
AT peregoarvid kobayashihitchincorrespondencefortwistedvectorbundles |
| _version_ |
1718371768773640192 |