On some properties of rank 2 reflexive sheaves on a smooth threefold

Abstract

We show that some properties of rank 2 reflexive sheaves true on P³ can be extended to a wide class of smooth projective threefolds. In particular, we establish some cohomological conditions in order that a rank 2 reflexive sheaf is locally free or a split bundle, or, equivalently, that an equidimensional, locally Cohen-Macaulay and generically local complete intersection curve lying on the threefold is subcanonical or a complete intersection.