Abstract.
Let X be a 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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Received: 16 September 2002 / Revised version: 15 November 2002 Published online: 3 March 2003
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Amerik, E. On endomorphisms of projective bundles. manuscripta math. 111, 17–28 (2003). https://doi.org/10.1007/s00229-002-0347-z
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DOI: https://doi.org/10.1007/s00229-002-0347-z