A Note on Normalizations of Orbit Closures

TL;DR

This paper provides a counterexample in the study of complex ternary cubic forms, showing that certain orbit closures do not have the normalization properties previously questioned by Landsberg.

Contribution

It offers a negative answer to Landsberg's question by constructing a counterexample related to orbit closures of complex ternary cubic forms.

Findings

Counterexample in orbit closure normalization

Negative answer to Landsberg's question

Implications for algebraic geometry of forms

Abstract

We give a negative answer to a question by J.M. Landsberg on the nature of normalizations of orbit closures. A counterexample originates from the study of complex, ternary, cubic forms.