Moduli of mathematical instanton vector bundles with even $c_2$ on projective space

We study the irreducibility problem for the moduli space $I_n$ of instanton vector bundles of rank 2 with second Chern class $n\geqslant1$ on the projective space $\mathbb{P}^3$ (the irreducibility of $I_n$ for odd values of $n$ was proved by the author in 2012). We prove that $I_n$ is irreducible for arbitrary even $n\geqslant2$. This gives the irreducibility of $I_n$ for all $n\geqslant1$.