Invariant Theory and Endomorphisms of Projective Bundles

Student: Kuznetsova Alexandra

Educational Programme: Mathematics (Bachelor)

Year of Graduation: 2016

Ekaterina Amerik in her paper ``On Endomorphisms of Projective Bundles'' has proved that if $X$ is a projectivisation of a vector bundle $E$ of rank 2 and we have an endomorphism of $X$ of degree more than one then $E$ splits after a finite base change. Now we will prove the same fact for projective bundles of higher dimensions in the situation when the first cohomology of any line bundle on the base vanishes.

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