Endomorphisms of projective bundles over a certain class of varieties
Bull. Korean Math. Soc. 2017 Vol. 54, No. 5, 1743-1755
https://doi.org/10.4134/BKMS.b160741
Published online September 30, 2017
Ekaterina Amerik, Alexandra Kuznetsova
Laboratory of Algebraic Geometry and Applications, Laboratory of Algebraic Geometry and Applications
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 $X=\p(E)$. 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.
Keywords : endomophisms, projective bundles, Newton polyhedra
MSC numbers : 14J60, 14L30
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