H-instanton bundles on three-dimensional polarized projective varieties

Abstract

We propose a notion of instanton bundle (called H-instanton bundle) on any projective variety of dimension three polarized by a very ample divisor H, that naturally generalizes the ones on P3 and on the flag threefold F(0,1,2). We briefly discuss the cases of Veronese and Fano threefolds. Then we deal with H-instanton bundles E on three-dimensional rational normal scrolls S(a0,a1,a2). We give a monadic description of H-instanton bundles and we prove the existence of μ-stable H-instanton bundles on S(a0,a1,a2) for any admissible charge k=c2(E)H. Then we deal in more detail with S(a,a,b) and S(a0,a1,a2) with a0+a1>a2 and even degree. Finally we describe a nice component of the moduli space of μ-stable bundles whose points represent H-instantons.