On curve sections of rank two reflexive sheaves

Abstract

Let F be a normalized rank 2 reflexive sheaf on P3 with Chern classes c 1,c 2,c 3. Let α be the least integer such that 0≠H 0 F(α) and β be the smallest integer such that H 0 F(n) has sections whose zero scheme is a curve for all n≥ β . We show that if T 0 is the largest root of the cubic polynomial then β ≥ T 0-α-c 1-1. There are applications to the smallest degree of a surface containing a curves which are the zero schemes of sections of H 0 F(α).