On branched coverings of some homogeneous spaces
Algebraic Geometry
2007-05-23 v1
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.
Keywords
Cite
@article{arxiv.math/9806126,
title = {On branched coverings of some homogeneous spaces},
author = {Meeyoung Kim and Laurent Manivel},
journal= {arXiv preprint arXiv:math/9806126},
year = {2007}
}
Comments
22 pages, LaTeX2e