On the GIT stratification of prehomogeneous vector spaces I

TL;DR

This paper characterizes the GIT stratification for four specific prehomogeneous vector spaces, providing a detailed parametrization of the stratification structure.

Contribution

It explicitly determines the GIT stratification sets for four prehomogeneous vector spaces, advancing understanding of their geometric and algebraic properties.

Findings

Explicit parametrization of GIT stratification sets

Enhanced understanding of prehomogeneous vector space structures

Foundation for further geometric invariant theory analysis

Abstract

We determine the set which parametrizes the GIT stratification for four prehomogeneous vector spaces in this paper.