On the moduli space \(M(0,4)\) of vector bundles (Q1109090)

Let \(M(c_1,c_2)\) denote the moduli space of vector bundles over \(\mathbb{P}^2_k\) of rank 2 with Chern classes \(c_1\) and \(c_2\) \((k\) an algebraically closed field of characteristic not 2). It has been proved by \textit{G. Ellingsrud} and \textit{S. A. Strømme} [``On the moduli space for stable rank-2 vector bundle on \(\mathbb{P}^2_k\)'' (Preprint, Oslo 1979)] that \(M(0,n)\) is rational for \(n\geq 3\), \(n\) odd. In this paper the author establishes that \(M(0,4)\) is rational.