1999/10/28 by Indranil Biswas, Biswas, Indranil, Christophe Mourougane +1
Mathematics · #14F05 (Primary) 32F05 (Secondary) #Advanced Algebra and Geometry #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Complex Variables (math.CV) #Differential Geometry (math.DG) #FOS: Mathematics #Geometry and complex manifolds #math.AG #math.CV #math.DG #msc:14F05 #msc:32F05
paper · pdf · doi:10.48550/arxiv.math/9910157
11 pages, Latex. Some remarks suggested by J.P. Demailly are added. To appear in the Duke Mathematical Journal
openalex publication_date 1999/10/28 · arxiv created 2000/04/10 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We prove that the L2 metric on the direct image of an adjoint positive line bundle by a locally trivial submersion between projective manifolds is Nakano positive, under the assumption that the typical fiber has zero first Betti number. As a consequence, we get that the symmetric powers of an ample vector bundle tensorized by its determinant are Nakano positive, in particular Griffiths positive. This in turn gives vanishing theorems and an analytic characterization of ample vector bundles.