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On endomorphisms of projective bundles

Ekaterina Amerik
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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.

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Ekaterina Amerik. 2002-09-18. On endomorphisms of projective bundles. https://arxiv.org/abs/math/0209220

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