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http://dx.doi.org/10.4134/BKMS.b160741

ENDOMORPHISMS OF PROJECTIVE BUNDLES OVER A CERTAIN CLASS OF VARIETIES

Amerik, Ekaterina (National Research University Higher School of Economics Laboratory of Algebraic Geometry and Applications)
Kuznetsova, Alexandra (National Research University Higher School of Economics Laboratory of Algebraic Geometry and Applications)

Publication Information

Bulletin of the Korean Mathematical Society / v.54, no.5, 2017 , pp. 1743-1755 More about this Journal

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.

Keywords

endomophisms; projective bundles; Newton polyhedra;

Citations & Related Records

Reference

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