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Статья

Endomorphisms of projective bundles over a certain class of varieties

Bulletin of the Korean Mathematical Society. 2017. Vol. 54. No. 5. P. 1743-1755.

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 = 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.