On moduli of instanton bundles on \(\mathbb{P}^{2n+1}\) (Q1918401)

Let \(\text{MI}_{\mathbb{P}^{2n+1}} (k)\) be the moduli space of stable instanton bundles of rank \(2n\) on \(\mathbb{P}^{2n+ 1}\) with \(c_2= k\). We prove that \(\text{MI}_{\mathbb{P}^{2n+ 1}} (2)\) is smooth and irreducible, as it happens for \(\mathbb{P}^3\). We find instead that \(\text{MI}_{\mathbb{P}^5} (3)\) and \(\text{MI}_{\mathbb{P}^5} (4)\) are similar, computing the dimension of the tangent space at some particular instanton bundles.