Stability and Hermitian-Einstein metrics for vector bundles on framed manifolds (Q2909609)
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scientific article; zbMATH DE number 6078196
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Stability and Hermitian-Einstein metrics for vector bundles on framed manifolds |
scientific article; zbMATH DE number 6078196 |
Statements
6 September 2012
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stability
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Hermitian--Einstein metric
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framed manifold
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Kähler--Einstein metric
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Stability and Hermitian-Einstein metrics for vector bundles on framed manifolds (English)
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The notions of stability of holomorphic vector bundle in the sense of Mumford-Takemoto and Hermitian-Einstein metric in holomorphic vector bundle are adapted for canonically polarized framed manifolds, i.e., compact complex manifolds \(X\) together with a smooth divisor \(D\) such that \(K_X\otimes [D]\) is ample. For stable holomorphic vector bundles the author obtains the existence of a Hermitian-Einstein metric with respect to \(g_{X\setminus D}\) and also the uniqueness in an adapted sense.
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