Abstract
A del Pezzo threefold F with maximal Picard number is isomorphic to P1×P1×P1. In the present paper we completely classify locally free sheaves E of rank 2 such that hi(F,E(t))=0 for i=1,2 and t∈Z. Such a classification extends similar results proved by E. Arrondo and L. Costa regarding del Pezzo threefolds with Picard number 1.
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