English

Iitaka fibrations for vector bundles

Algebraic Geometry 2017-01-27 v2

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.

Keywords

Cite

@article{arxiv.1611.09585,
  title  = {Iitaka fibrations for vector bundles},
  author = {Ernesto C. Mistretta and Stefano Urbinati},
  journal= {arXiv preprint arXiv:1611.09585},
  year   = {2017}
}

Comments

Edit for second version: the final remark was removed, as it was not correct. Some questions and a theorem added in the last section

R2 v1 2026-06-22T17:07:47.874Z