Abstract
In this section we introduce the crucial concept of stability of holomorphic vector bundles over ℙ n . We begin by collecting together several theorems about torsion-free, normal and reflexive sheaves which we shall need later. Then we define stable and semistable torsion-free sheaves in the sense of Mumford and Takemoto and compare this concept of stability with that of \(\mathcal{O}_{\mathbb{P}n} \) (1)-stability as introduced by Gieseker and Maruyama. In a final section we investigate the stability of a number of bundles with which we became acquainted in earlier sections.
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