As stated, Theorem 2.4 is incorrect. Indeed, as shown in forthcoming work of Alheydis Geiger and Francesca Zaffalon an open part of the orthogonal Grassmannian $\mathrm{OGr}(n,2n)$ is $2^{n-1}$ to 1 to the self-dual configuration space $\mathcal{S}(n)=X(n,2n)^{\mathrm{sd}}$. Since $\mathrm{SO}(n)$ is birational to one of the connected components of the orthogonal Grassmannian $\mathrm{OGr}(n,2n)$, the map from $\mathrm{SO}(n)$ to $X(n,2n)^{\mathrm{sd}}$ defined by sending an orthogonal matrix $R$ to $(I|R)$ is only finite to 1, but not injective. However, the main consequence of the theorem (“$\mathcal{S}(n)$ is rational and of dimension $\binom{n}{2}$”), stated in Corollary 2.5, was proven in Dolgachev-Ortland and therefore remains correct.