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arXiv · 1611.09585

Iitaka fibrations for vector bundles

Ernesto C. Mistretta·Stefano Urbinati
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Abstract

A vector bundle on a smooth projective variety, if it is generically generated by global sections, yields a rational map to a Grassmannian, called Kodaira map. We investigate the asymptotic behaviour of the Kodaira maps for the symmetric powers of a vector bundle, and we show that these maps stabilize to a map dominating all of them, as it happens for a line bundle via the Iitka fibration. Through this Iitaka-type construction, applied to the cotangent bundle, we give a new characterization of Abelian varieties.

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Ernesto C. Mistretta, Stefano Urbinati. 2016-11-29. Iitaka fibrations for vector bundles. https://arxiv.org/abs/1611.09585

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