The splitting criterion of Kempf and the Babylonian tower theorem

2004/11/29 by Iustin Coanda, Coanda, Iustin, Guenther Trautmann +1
Mathematics · #14F05 #14J60 #Algebraic Geometry (math.AG) #FOS: Mathematics #math.AG #msc:14F05 #msc:14J60

paper · pdf · doi:10.48550/arxiv.math/0411636

LateX2e, 4 pages

arxiv created 2004/11/29 · arxiv updated 2009/12/01

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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