On the GIT stratification of prehomogeneous vector spaces III

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.