The boundary of the orbit of the 3 by 3 determinant polynomial

TL;DR

This paper characterizes the boundary of the orbit of the 3x3 determinant polynomial under linear transformations, providing insights into its limit points and answering a question posed by Landsberg.

Contribution

It describes the boundary and limit points of the orbit of the 3x3 determinant polynomial under linear changes, advancing understanding of its geometric properties.

Findings

Identified the boundary of the orbit of the 3x3 determinant polynomial.

Described the limit points of the orbit under linear transformations.

Answered Landsberg's question on the orbit's boundary.

Abstract

We consider the 3 by 3 determinant polynomial and we describe the limit points of the set of all polynomials obtained from the determinant polynomial by linear change of variables. This answers a question of J. M. Landsberg.