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Ample vector bundles and branched coverings

Thomas Peternell·Andrew J. Sommese
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Abstract

Given a covering f: X \to Y of projective manifolds, we consider the vector bundle E on Y given as the dual of f_*(Ø_X) / Ø_Y. This vector bundles often has positivity properties, e.g. E is ample when Y is projective space by a theorem of Lazarsfeld. In general however E will not be ample due to the geometry of Y. We prove various results when E is spanned, nef or generically nef, under some assumptions on the base Y.

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Thomas Peternell, Andrew J. Sommese. 1999-07-13. Ample vector bundles and branched coverings. https://arxiv.org/abs/math/9907081

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