2011•Advances in GeometryRequires access

Ample vector bundles and polarized manifolds of sectional genus three

Luca Benzo, Antonio Lanteri

Abstract

Abstract Let ℰ be an ample vector bundle of rank r ≥ 2 on a smooth complex projective variety X of dimension n having a global section whose zero locus Z is a smooth subvariety of dimension n – r ≥ 3 of X. Let H be an ample line bundle on X such that its restriction HZ to Z is generated by global sections. The structure of triplets (X, ℰ, H) is determined under the assumption that (Z, HZ ) has sectional genus g(Z, HZ ) = 3.

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Key concepts: Subvariety, Vector bundle, Mathematics, Ample line bundle, Projective variety, Line bundle, Dimension (graph theory), Rank (graph theory)