Globally generated fibre bundles over the projective space
\textit{P. Ellia} and \textit{A. Hirschowitz} recently [cf. J. Algebr. Geom. 1, No. 4, 531-547 (1992; Zbl 0812.14036)] suggested that a ``general'' fiber bundle of rank \(r\) on a smooth projective \(n\)-dimensional variety should be globally generated as soon as it possesses \(n + r\) independent global sections. This principle would provide a useful complement to the classical Castelnuovo-Mumford criterion. We prove a conjecture of \textit{A. Dolcetti} [Math. Ann. 294, No. 1, 99-107 (1992; Zbl 0782.14017)] that this principle holds true for vector bundles on \(\mathbb{P}^ n\) constructed as kernels of generic morphisms from \({\mathcal O}_{\mathbb{P}^ n} (d)^{\oplus b}\) to \({\mathcal O}_{\mathbb{P}^ n} (d + 1)^{\oplus a}\). These bundles are twisted duals of Steiner bundles, following the terminology of Dolgachev and Kapranov. Our proof relies on a careful dimension count for the exceptional sets of such morphisms.
scientific article; zbMATH DE number 759278