Some vanishing properties of the intermediate cohomology of a reflexive sheaf on \(\mathbb{P}^ n\)
Let \(F\) be a vector bundle or a reflexive sheaf on \(\mathbb{P}_3\). The paper is devoted to the study of some vanishing properties of the intermediate cohomology of \(F\). Most of the results of the paper repeat well-known results, for example, from \textit{L. Chiantini} and \textit{P. Valabrega} [Ann. Mat. Pura Appl., IV. Ser. 138, 309-330 (1984; Zbl 0569.14014)]. The authors' approach, in contrast with the previously published papers on the subject, involves the notion of the spectrum of \(F\). This gives some additional estimates for \(h^2F (m)\) and eliminates the restriction on the characteristic of the base field.
vanishing properties of the intermediate cohomology
scientific article; zbMATH DE number 703033