Ulrich bundles on Del Pezzo threefolds

We prove that for any r⩾2 the moduli space of stable Ulrich bundles rank r and determinant OX(r) on smooth Fano threefold X index two is dimension r2+1 same holds true even when four, in which case no odd–rank exist. In particular this shows such wild. As a preliminary result, we give necessary sufficient conditions existence projective terms curve enjoying special properties.