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Iskovskikh Seminar
October 6, 2016 18:00, Moscow, Steklov Mathematical Institute, room 540
 


Endomorphisms of projective bundles

Alexandra Kuznetsova

State University – Higher School of Economics

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Abstract: Let $B$ be a simply-connected projective variety such that the first cohomology groups of all line bundles on $B$ are zero. Let $E$ be a vector bundle over $B$ and $X={\mathbb P} (E)$. It is easily seen that a power of any endomorphism of $X$ takes fibers to fibers. We prove that if $X$ admits an endomorphism which is of degree greater than one on the fibers then $E$ splits into a direct sum of line bundles.

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