Moduli spaces of rank-2 ACM bundles on prime Fano threefolds

Abstract

Given a smooth non-hyperelliptic prime Fano threefold X, we prove the ex- istence of all rank 2 ACM vector bundles on X by deformation of semistable sheaves. We show that these bundles move in generically smooth components of the corresponding moduli space. We give applications to pfaffian representations of quartic t in P 4 and cubic hypersurfaces of a smooth quadric of P 5 .