GIT-equivalence and diagonal actions

Abstract

We describe the GIT-equivalence classes of linearized ample line bundles for the diagonal actions of the linear algebraic groups $SL(V)$ and $SO(V)$ on ${\mathbb{P}(V)^{m_1}\times \mathbb{P}(V^*)^{m_2}}$ and $\mathbb{P}(V)^m$ respectively.