Moduli spaces of rank 2 ACM bundles on prime Fano threefolds

TL;DR

This paper proves the existence and describes the moduli spaces of rank 2 ACM bundles on prime Fano threefolds, with applications to pfaffian representations of certain threefolds and hypersurfaces.

Contribution

It establishes the existence of all rank 2 ACM bundles on prime Fano threefolds via deformation theory and analyzes their moduli space components.

Findings

All rank 2 ACM bundles exist on prime Fano threefolds.

Bundles form generically smooth moduli space components.

Applications to pfaffian representations of quartic threefolds and cubic hypersurfaces.

Abstract

Given a smooth non-hyperelliptic prime Fano threefold X, we prove the existence 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 threefolds in P^4 and cubic hypersurfaces of a smooth quadric of P^5.