DEFORMATIONS OF REFLEXIVE SHEAVES OF RANK 2 ON P³.

Jan O. Kleppe

In this paper we study deformations of reflexive sheaves of rank 2 on P = P³ . Let F be a reflexive sheaf with a section s of H⁰(P,F) whose corresponding scheme of zeros is a curves C in P, and let M = M(c₁,c₂,c₃) be the (coarse) moduli space of stable reflexive sheaves with Chern classes c₁, c₂ and c₃. The study of how the deformations of the space curve C correspond to the deformations of the reflexive sheaf F leads to a nice relationship between the local ring O_H,C of the Hilbert scheme H = H(d,g) of curves of degree d and arithmetic genus g at C , and the corresponding the local ring O_M,F of M at F. In this paper we consider several examples where we use this relationship. In particular we prove that the moduli spaces M(0,13,74) and M(-1,14,88) contain generically non-reduced components.