On jumping lines of vector bundles on \(\mathbb {P}^n\) (Q2364521)

Let \(E\) be a vector bundle on \(\mathbb {P}^n\). \(E\) is said to be \textit{almost uniform} if it has only finitely jumping lines and at least one jumping line. Call \(A(n)\) the minimum rank of an almost uniform vector bundle on \(\mathbb {P}^n\). The main result of this paper is the proof that \(A(2) =2\) and that \(n+1 \leq A(n) \leq 2n-1\) for all \(n>2\). The author suggests that the correct value of \(A(n)\) should be very near to \(2n-1\).