On the existence of generically smooth components for moduli spaces of rank 2 stable reflexive sheaves on P3

Abstract

The goal of this work is to prove that for almost all possible triples ( c 1, c 2, c 3) ϵ Z 3 the moduli scheme M(2; c 1, c 2, c 3), which parametrizes isomorphism classes of rank 2 stable reflexive sheaves on P 3 with Chern classes c 1, c 2 and c 3, has a generically smooth component. In order to obtain these results we construct a wide range of non-obstructed, m-normal curves with suitable degree and genus. We conclude this paper by adding some examples and remarks.