Instanton bundles on two Fano threefolds of index 1

Abstract

Abstract We deal with instanton bundles on the product ℙ 1 × ℙ 2 {\mathbb{P}^{1}\times\mathbb{P}^{2}} and the blow up of ℙ 3 {\mathbb{P}^{3}} along a line. We give an explicit construction leading to instanton bundles. Moreover, we also show that they correspond to smooth points of a unique irreducible component of their moduli space.