On endomorphisms of projective bundles

Ekaterina Amerik

On endomorphisms of projective bundles

Algebraic Geometry 2007-05-23 v1

Authors: Ekaterina Amerik

Abstract

Let $X$ be a complex projective bundle. We prove that $X$ admits an endomorphism of degree $>1$ and commuting with the projection to the base, if and only if $X$ trivializes after a finite covering. When $X$ is the projectivization of a vector bundle $E$ of rank 2, we prove that it has an endomorphism of degree $>1$ on a general fiber only if $E$ splits after a finite base change.

Keywords

vector bundles projective varieties bundle theory

Cite

@article{arxiv.math/0209220,
  title  = {On endomorphisms of projective bundles},
  author = {Ekaterina Amerik},
  journal= {arXiv preprint arXiv:math/0209220},
  year   = {2007}
}

Comments

LaTeX 2.09, 13 pages

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