Abstract
It was some years ago that Grauert posed the problem to find an example of a smooth space curve whose normal bundle is indecomposable. The first to produce such an example was Van de Ven [3]. He studied space curves C of degree 5 and genus 2. Such a curve lies necessarily on an irreducible quadric Q. If Q is smooth then C has bidegree (2, 3) or (3, 2) and its normal bundle N c does not split. If, however, Q is a quadric cone then N c does in fact split. The whole purpose of this note is to point out that the situation described by Van de Ven is typical for curves on quadrics. We shall prove:
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