Homogeneous instanton bundles on [formula omitted] for the action of [formula omitted

Abstract

We classify k -instanton bundles on P C 3 which are homogeneous for the group SL ( 2 ) , acting linearly on P 3 with an open orbit. Besides the classical special instantons, we find isolated examples for SL ( 2 ) acting by the representation of binary cubics. We show that these examples are unique and that they exist only for k = a ( a − 1 ) / 2 , for some a ≥ 2 . We also compute their minimal free resolution in terms of homogeneous equivariant matrices.