Semiample and k-ample vector bundles |
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Authors: | F. Laytimi W. Nahm |
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Affiliation: | 1. Faculte de Sciences et Technologie, Département de Mathématiques, Cité scientifique – Batiment, Université de Lille, Villeneuve d’Ascq Cedex, France;2. fatima.laytimi@univ-lille.fr;4. Dublin Institute for Advanced Studies, Dublin, Ireland |
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Abstract: | AbstractThe main result of this paper is that tensor products of semiample vector bundles over compact complex manifolds are semiample. An easy proof yields the analogous result for direct sums. We also show that tensor products of semiample vector bundles with k-ample vector bundles in the sense of Sommese are k-ample. On the other hand, we show that it is not generally true that tensor products of nef and k-ample vector bundles for positive k are still k-ample. Results of Sommese on k-ampleness are consequently strengthened. As an application of our main theorem we extend to k-ample the vanishing theorem of Ein-Lazarsfeld. |
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Keywords: | Semiampleness vanishing theorems vector bundles |
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