Instanton Bundles on the Blowup of the Projective 3-Space at a Point

Abstract

We propose a general definition of mathematical instanton bundle with given charge on any Fano threefold extending the classical definitions on ${\mathbb{P}}^3$ and on Fano threefold with cyclic Picard group. Then we deal with the case of the blowup of ${\mathbb{P}}^3$ at a point, giving an explicit construction of instanton bundles satisfying some important extra properties. Moreover, we show that they correspond to smooth points of a component of the moduli space.