On rank 3 instanton bundles on P3$\mathbb {P}^3$

Abstract

AbstractWe investigate rank 3 instanton vector bundles on of charge and its correspondence with rational curves of degree . For , we present a correspondence between stable rank 3 instanton bundles and stable rank 2 reflexive linear sheaves of Chern classes 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 of charge 2 coincides with the moduli space of rank 3 stable locally free sheaves on of Chern classes . This moduli space is irreducible, has dimension 16 and its generic point corresponds to a generalized't Hooft instanton bundle.