Biliaison Classes of Rank Two Reflexive Sheaves on P 3

A biliaison theory for rank two reflexive sheaves on projective 3 ‐ space is established, In analogy with the existing theory for curves and, more generally, for 2 ‐ codimensional subschemes of projective n ‐ space. By definition two such sheaves are in the same biliaison class if their first cohomology modules are isomorphic. A parametrization of these classes is given. It is then shown that any class not corresponding to the zero module has a structure described by the Lazarsfeld ‐ Rao property. In particular, it is shown that vector bundles are precisely the minimal elements (in the of the LR ‐ property) in their biliaison classes.