Stable Ulrich bundles on Fano threefolds with Picard number 2

In this paper, we consider the existence problem of rank one and two stable Ulrich bundles on imprimitive Fano 3-folds obtained by blowing-up one of P-3, Q (smooth quadric in P-4), V-3 (smooth cubic in P-4) or V-4 (complete intersection of two quadrics in P-5) along a smooth irreducible curve. We prove that the only class which admits Ulrich line bundles is the one obtained by blowing up a genus 3, degree 6 curve in P-3. Also, we prove that there exist stable rank two Ulrich bundles with c(1) = 3H on a generic member of this deformation class. (C) 2017 Elsevier B.V. All rights reserved.