Rationality of moduli spaces of vector bundles on rational surfaces

Abstract

Let $X$ be a smooth rational surface. In this paper, we prove the rationality of the moduli space ${M}_{X, L}(2; c_{1}, c_{2})$ of rank two $L$-stable vector bundles $E$ on $X$ with det $(E) = c_{1} \in $ Pic$(X)$ and $c_{2}(E) = c_{2} \gg 0$.