Irreducibility of the moduli space $I_n$ of mathematical instanton vector bundles on the projective space $P_3$ for arbitrary odd second Chern class $n$

The problem of description of the moduli space $I_n$ of mathematical instanton vector bundles on the projective space $P_3$ has been a challenging problem since 70's. It was conjectured by R.Hartshorne in 1976 that $I_n$ is irreducible for an arbitrary second Chern class $n>0$. This problem has an affirmative solution for small values of $n$, up to $n=5$. Namely, the cases $n=1,2,3,4$ and 5 were settled by Barth (1977), Hartshorne (1978), Ellingsrud-Stromme (1981), Barth (1981) and Coanda-Tikhomirov-Trautmann (2003), respectively. The aim of this talk is to give a proof of the irreducibility of $I_n$ for arbitrary odd second Chern class $n$".