Das Spektrum torsionsfreier Garben. I
In this paper, the authors study torsion-free sheaves of arbitrary rank on projective spaces, and in particular generalize some of R. Hartshorne's techniques and results [\textit{R. Hartshorne}, Math. Ann. 254, 121-176 (1980; Zbl 0431.14004); Invent. Math. 66, 165-190 (1982; Zbl 0519.14008)] which were originally developed for the more restricted classes of reflexive sheaves of rank 2. The study of torsion-free sheaves is important since these occur naturally in the compactifications of the moduli spaces of stable vector bundles and also as the ideal sheaves of projective varieties. The principal object of this paper is to generalize the concept of spectrum to an arbitrary torsion-free sheaf F on \({\mathbb{P}}^ 3\); this leads to inequalities for the second and third Chern classes of F similar to those which hold in the reflexive case. The authors also study the annihilators of certain cohomology classes, and hence prove under suitable conditions the existence of unstable planes for F.
compactifications of the moduli spaces of stable vector bundles
scientific article; zbMATH DE number 3889699