Ample vector bundles and applications

00:00 08-02-2006

We will introduce, in the context of complex algebraic varieties, the notion of ample vector bundles. Vector bundles are defined roughly as families of fixed rank vector spaces parameterized by the points of an algebraic variety. In the case of rank 1 vector bundles, amplitude is equivalent to the existence of a metric of positive curvature (Kodaira), but it is still unknown if this can be generalized to higher ranks. We will focus instead on definition and properties of ample vector bundles derived from intersection theory. We will link the ampleness property of some natural vector bundles (like the tangent and cotangent bundles) to hyberbolicity and topological properties. We will give applications to the problem of classification of algebraic varieties and also to the Picard variety of algebraic curves.

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