Faisceaux semi-stables de rang 2 sur P3

Abstract

The authors consider semistable sheaves (in the sense of Mumford-Takemoto) of rank 2 on P3. By studying sections, they are able to determine all Chern classes c1,c2,c3 for which such sheaves exist. As an application they describe a stratification of the moduli space MP2(−1,c2) of stable rank 2 sheaves on P2 with given Chern classes c1=−1 and c2. This space can be viewed as a compactification of the moduli space of stable rank 2 vector bundles over the projective plane.