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Let P^n be the projective space of dimension n on an algebraically closedfield of characteristic 0 and F be the image of the Segre embedding ofP^1xP^1xP^1 inside P^7. In the present paper we deal with the moduli spaces oflocally free sheaves E on F of rank 2 with h^i(F,E(t))=0 for i=1,2 and eachinteger t.

Moduli spaces of rank two aCM bundles on the Segre product of three projective lines