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

Abstract

Given a smooth non-hyperelliptic prime Fano threefold X, we prove the\nexistence of all rank 2 ACM vector bundles on X by deformation of semistable\nsheaves. We show that these bundles move in generically smooth components of\nthe corresponding moduli space. We give applications to pfaffian\nrepresentations of quartic threefolds in P^4 and cubic hypersurfaces of a\nsmooth quadric of P^5.\n