Ample vector bundles with sections vanishing on special varieties

Details Ample vector bundles with sections vanishing on special varieties Ample vector bundles with sections vanishing on special varieties

1998-07-16

arxiv.org/abs/math/9807082v2

Mathematics

Algebraic Geometry

Some minor changes, added refrences for section 2, 21 pages, to appear on International Journal of Mathematics

Scientific paper

Let E be an ample vector bundle of rank r on a complex projective manifold X such that there exists a section $s \in \Gamma(\cal E)$ 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.

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