Rank two aCM bundles on the del Pezzo threefold with Picard number 3

TL;DR

This paper classifies rank 2 aCM bundles on the del Pezzo threefold P^1 x P^1 x P^1, extending previous classifications to the case of maximal Picard number.

Contribution

It provides a complete classification of rank 2 aCM bundles on the del Pezzo threefold with Picard number 3, a case not previously fully understood.

Findings

Classification of rank 2 aCM bundles on P^1 x P^1 x P^1

Extension of previous results to maximal Picard number case

Complete description of such bundles' properties

Abstract

Let k be an algebraically closed field of characteristic 0. A del Pezzo threefold F with maximal Picard number is isomorphic to P^1xP^1xP^1, where P^1 is the projective line over k. In the present paper we completely classify locally free sheaves of rank 2 with vanishing intermediate cohomology over such an F. Such a classification extends similar results proved by E. Arrondo and L. Costa regarding del Pezzo threefolds with Picard number 1.