Globally generated vector bundles on the del Pezzo threefold of degree 6 with Picard number 2 (Q6544726)

There are a few papers (quoted in the paper under review) on the classification of globally generated vector bundles with low \(c_1\) on a Fano 3-fold. Let \(X\) be a general hyperplane section of \(\mathbb{P}^2\times \mathbb{P}^2\). The author gives the complete list of the possible second Chern number \((e_1,e_2)\in \mathbb{N}^2\) and rank \(r\) of a globally generated vector bundle \(E\) with \(c_1(E)\) either \((1,1)\) or \((2,1)\) without a trivial factor (they exists if and only if \(r\le 14\)). In a few cases there is also a description of the possible bundles \(E\). The proof uses the Serre correspondence and the study of curves on \(\mathbb{P}^2\times \mathbb{P}^2\) with low bidegree.