GIT-Equivalence and Diagonal Actions

In the paper, the GIT-equivalence classes of the linearized linear bundles for the diagonal actions of the linear algebraic groups $\operatorname{SL}(V)$ and $\operatorname{SO}(V)$ on the projective varieties $\mathbb{P}(V)^{m_1}\times\mathbb{P}(V^*)^{m_2}$ and $\mathbb{P}(V)^m$, respectively, are described explicitly.