

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 simplyconnected 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.

