1998/06/23 by Meeyoung Kim, Mee-Young Kim, Kim, Meeyoung +2
Mathematics · #Advanced Algebra and Geometry #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics #Meromorphic and Entire Functions #math.AG
paper · pdf · doi:10.48550/arxiv.math/9806126
22 pages, LaTeX2e
arxiv created 1998/06/23 · openalex publication_date 1998/06/23 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.