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 July 26, 2017 Printed 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
