On rank 3 instanton bundles on P 3 $\mathbb {P}^3$

Abstract

We investigate rank 3 instanton vector bundles on $P^3$ of charge $n$ and its correspondence with rational curves of degree $n+3$. For $n=2$, we present a correspondence between stable rank 3 instanton bundles and stable rank 2 reflexive linear sheaves of Chern classes $(c_1,c_2,c_3)=(-1,3,3)$ and we use this correspondence to compute the dimension of the family of stable rank 3 instanton bundles of charge 2. Finally, we use the results above to prove that the moduli space of rank 3 instanton bundles on $P^3$ of charge 2 coincides with the moduli space of rank 3 stable locally free sheaves on $P^3$ of Chern classes $(c_1,c_2,c_3)=(0,2,0)$. This moduli space is irreducible, has dimension 16 and its generic point corresponds to a generalized't Hooft instanton bundle.