The splitting criterion of Kempf and the Babylonian tower theorem

Details The splitting criterion of Kempf and the Babylonian tower theorem The splitting criterion of Kempf and the Babylonian tower theorem

2004-11-29

arxiv.org/abs/math/0411636v1

Mathematics

Algebraic Geometry

LateX2e, 4 pages

Scientific paper

We show that the idea used by Kempf (1990) in order to obtain a splitting criterion for vector bundles on projective spaces leads to an elementary proof of the Babylonian tower theorem for this class of bundles, a result due to Barth--Van de Ven (1974) in the rank 2 case and to Sato (1977) and Tyurin (1976) in the case of arbitrary rank. As a byproduct we obtain a slight improvement of the numerical criterion of Flenner (1985) in the particular case under consideration.

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