Let ε be an ample vector bundle of rank r on a complex projective manifold X such that there exists a section s ∈ P(ε) whose zero locus Z = (s = 0) is a smooth submanifold of the expected dimension dim X - r := n - r. Assume that Z is not minimal; we investigate the hypothesis under which the extremal contractions of Z can be lifted to X. Finally we study in detail the cases in which Z is a scroll, a quadric bundle or a del Pezzo fibration.
Ample vector bundles with sections vanishing on special varieties
Andreatta, Marco;Occhetta, Gianluca
1999-01-01
Abstract
Let ε be an ample vector bundle of rank r on a complex projective manifold X such that there exists a section s ∈ P(ε) whose zero locus Z = (s = 0) is a smooth submanifold of the expected dimension dim X - r := n - r. Assume that Z is not minimal; we investigate the hypothesis under which the extremal contractions of Z can be lifted to X. Finally we study in detail the cases in which Z is a scroll, a quadric bundle or a del Pezzo fibration.File in questo prodotto:
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