Construction of rank two vector bundles on \(\mathbb{P}^{4}\) in positive characteristic
The main result of this paper is the construction in positive characteristic of several rank two non-splitted vector bundles on \(\mathbb{P}^4\) (even with the same Chern classes as the Horrocks-Mumford bundle, but different from it). The main tool is a characteristic free new criterion for the extension to \(\mathbb{P}^{n+1}\) of a bundle defined on the \(m\)-th thickening of a hyperplane of \(\mathbb{P}^{n+1}\). As remarked by the author it is very difficult to apply this criterion outside the very interesting case applied in this paper for the construction of these new bundles in \(\mathbb{P}^4\).
non-splitted vector bundles on \(\mathbb{P}^4\)
scientific article; zbMATH DE number 1096052