On the GIT stratification of prehomogeneous vector spaces III

TL;DR

This paper classifies all orbits of a specific prehomogeneous vector space involving general linear groups over any perfect field, advancing understanding of its algebraic structure.

Contribution

It provides a complete orbit classification for the GIT stratification of the given prehomogeneous vector space over arbitrary perfect fields.

Findings

All orbits of the vector space are explicitly determined.

The classification holds over any perfect field, not just algebraically closed fields.

The results facilitate further geometric and algebraic analysis of the space.

Abstract

We determine all orbits of the prehomogeneous vector space $(\mathrm{GL}_5\times \mathrm{GL}_4,\wedge^2\mathrm{Aff}^5 \otimes \mathrm{Aff}^4)$ rationally over an arbitrary perfect field in this paper.