The splitting criterion of Kempf and the Babylonian tower theorem

Iustin Coanda; Guenther Trautmann

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The splitting criterion of Kempf and the Babylonian tower theorem

Iustin Coanda·Guenther Trautmann

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Abstract

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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Iustin Coanda, Guenther Trautmann. 2004-11-29. The splitting criterion of Kempf and the Babylonian tower theorem. https://arxiv.org/abs/math/0411636

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