Invariants of ample vector bundles on smooth projective varieties
Received: 27 April 2011
Accepted: 19 May 2011
Mathematics Subject Classification (2010): Primary 14J60; Secondary 14C17, 14C20, 14C40, 14J30, 14J35, 14J40.
Keywords: Ample vector bundle, ample line bundle, (multi-)polarized manifold, (multi-)generalized polarized manifold, sectional geometric genus, sectional H-arithmetic genus, sectional Euler number, sectional Betti number, sectional Hodge number.
Abstract: Let X be a smooth projective variety of dimension n, let ε be an ample vector bundle of rank r on X with 1 ≤ r ≤ n. Then we are going to introduce some invariants of (X,ε) which are considered to be a generalization of invariants of polarized manifolds we introduced before. Moreover we will study some properties of these and some relationships between these.