Ample vector bundles and branched coverings

1999/07/13 by Thomas Peternell, Peternell, Thomas, Andrew J. Sommese +1
Mathematics · #14E20 #14J60 #Algebraic Geometry (math.AG) #FOS: Mathematics #math.AG #msc:14E20 #msc:14J60

paper · pdf · doi:10.48550/arxiv.math/9907081

LaTeX2e, 26 pages

arxiv created 1999/07/13 · arxiv updated 2009/11/30

Abstract

Given a covering f: X → 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.

Related

• Ample Vector Bundles and Branched Coverings, II
• On branched coverings of some homogeneous spaces
• Ampleness equivalence and dominance for vector bundles
• Criteria for the ampleness of certain vector bundles
• Positivity of vector bundles on homogeneous varieties