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Power generatedness of a holomorphic line bundle and an application to complex-contact manifolds

Osami Yasukura
Arxiv ID: 0905.2656Last updated: 9/29/2022
A holomorphic line bundle on a complex manifold is said to be power generated when every positive integer $m$ satisfies that any holomorphic section for the $m$-th tensor power of the bundle is the $m$-th tensor power of some holomorphic section for the bundle. A power generated holomorphic line bundle is very ample if it is ample. We obtain that a holomorphic line bundle is power generated provided that the base manifold is connected, simply connected and paracompact. As an application, we obtain that every connected Fano complex-contact manifold is isomorphic to some kaehlerian C-space of Boothby type with the natural complex-contact distribution, and that any positive quaternionic Kaehler manifold is equivalent to the Wolf space for some simple compact Lie algebra of rank greater than one.

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