GIT-equivalence and diagonal actions

TL;DR

This paper classifies GIT-equivalence classes of linearized line bundles for diagonal group actions of SL(V) and SO(V) on products of projective spaces, advancing understanding of geometric invariant theory in these contexts.

Contribution

It provides a detailed description of GIT-equivalence classes for specific diagonal actions of SL(V) and SO(V) on products of projective spaces.

Findings

Classified GIT-equivalence classes for SL(V) actions.

Classified GIT-equivalence classes for SO(V) actions.

Enhanced understanding of GIT stability conditions.

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.