Contractions on a manifold polarized by an ample vector bundle

ar X iv : a lg - g eo m / 9 41 00 29 v 1 2 7 O ct 1 99 4 Contractions on a manifold polarized by an ample vector bundle

Vector Bundles on Hirzebruch Surfaces Whose Twists by a Non-ample Line Bundle Have Natural Cohomology

Here we study vector bundles E on the Hirzebruch surface Fe such that their twists by a spanned, but not ample, line bundle M = OFe(h + ef) have natural cohomology, i.e. h(Fe, E(tM)) > 0 implies h(Fe, E(tM)) = 0.

On subvarieties with ample normal bundle

We show that a pseudoeffective R-divisor has numerical dimension 0 if it is numerically trivial on a subvariety with ample normal bundle. This implies that the cycle class of a curve with ample normal bundle is big, which gives an affirmative answer to a conjecture of Peternell. We also give other positivity properties of such subvarieties.

A Positivity Property of Ample Vector Bundles

Using Fujita-Griffiths method of computing metrics on Hodge bundles, we show that for every semi-ample vector bundle E on a compact complex manifold, and every positive integer k, the vector bundle SE ⊗ detE has a continuous metric with Griffiths semi-positive curvature. If E is ample, the metric can be made smooth and Griffiths positive.

ON THE LIFTS OF SEMI-RIEMANNIAN METRICS

In this paper, we extend Sasaki metric for tangent bundle of a Riemannian manifold and Sasaki-Mok metric for the frame bundle of a Riemannian manifold [I] to the case of a semi-Riemannian vector bundle over a semi- Riemannian manifold. In fact, if E is a semi-Riemannian vector bundle over a semi-Riemannian manifold M, then by using an arbitrary (linear) connection on E, we can make E, as a...