ar X iv : m at h / 00 02 16 9 v 1 [ m at h . A G ] 2 1 Fe b 20 00 MINIMAL RESOLUTION OF GENERAL STABLE VECTOR BUNDLES ON

In this paper we investigate stable vector bundles on the complex projective plane P by means of their minimal free resolution. The fundamental background for this study is the work of Bohnhorst and Spindler [BS92] and their idea to use admissible pairs to characterize the stability of rank-n vector bundles on P and to give a stratification of the relative moduli space in constructible subsets. Two main difficulties arise: (i) to state a weak version of the Bohnhorst-Spindler theorems for rank r ≥ 2 vector bundles on P, (ii) to estimate the codimension of the constructible subsets of the moduli space. In section 2 we make some general remarks on rank r vector bundles on P with r ≥ n to address (i), while (ii) is the object of the last section. We would like to thank G. Ottaviani for his invaluable guidance and V. Ancona for many useful discussions.