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 ∈ Pic(X) and c 2 (E) = c 2 ≫ 0.