On the rationality of the moduli space of instanton bundles on the projective 3-space

We prove the rationality and irreducibility of the moduli space of—what we call—the endomorphism-general instanton vector bundles of arbitrary rank on the projective space. In particular, we deduce the rationality of the moduli spaces of rank-two mathematical instantons. This problem was first studied by Hartshorne, Hirschowitz-Narasimhan in the late 1970s, and it has been reiterated within the framework of the ICM 2018.