A note on pseudo-effective vector bundles with vanishing first Chern number over non-Kähler manifolds
In this note, We show that over a compact Hermitian manifold $(X, \omega )$ whose metric satisfies $\partial \bar{\partial }\omega ^{n - 1} = \partial \bar{\partial }\omega ^{n - 2} = 0$, every pseudo-effective vector bundle with vanishing first Chern number is in fact a numerically flat vector bund...
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| Format: | Article |
| Language: | English |
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Académie des sciences
2021-07-01
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| Series: | Comptes Rendus. Mathématique |
| Online Access: | https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.5802/crmath.182/ |
| Summary: | In this note, We show that over a compact Hermitian manifold $(X, \omega )$ whose metric satisfies $\partial \bar{\partial }\omega ^{n - 1} = \partial \bar{\partial }\omega ^{n - 2} = 0$, every pseudo-effective vector bundle with vanishing first Chern number is in fact a numerically flat vector bundle. |
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| ISSN: | 1778-3569 |