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On branched coverings of some homogeneous spaces

Meeyoung Kim·Laurent Manivel
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Abstract

We study nonsingular branched coverings of a homogeneous space X. There is a vector bundle associated with such a covering which was conjectured by O. Debarre to be ample when the Picard number of X is one. We prove this conjecture, which implies Barth-Lefschetz type theorems, for lagrangian grassmannians, and for quadrics up to dimension six. We propose a conjectural extension to homogeneous spaces of Picard number larger than one and prove a weaker version.

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Meeyoung Kim, Laurent Manivel. 1998-06-23. On branched coverings of some homogeneous spaces. https://arxiv.org/abs/math/9806126

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