Bundles on the Fano threefold V_5
  Using an explicit resolution of the diagonal for the variety V_5, we provide cohomological characterizations of the universal and quotient bundles. A splitting criterion for bundles over V_5 is also proved.   The presentation of semistable aCM (i.e. with no intermediate cohomology) bundles is shown, together with a resolution-theoretic classification of low rank aCM bundles. 
Daniele Faenzi