A Note on normalizations of orbit closures

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.

KEYWORDS:

• Birational geometry
• classical groups
• geometric complexity theory

2010 MATHEMATICS SUBJECT CLASSIFICATION:

• 14L24
• 13A50

Acknowledgment

I thank Peter Bürgisser very much for his many helpful comments about this note. I also extend my gratitude to J. M. Landsberg for his encouragement and several related discussions. Finally, I am grateful to Christian Ikenmeyer for providing Formula (5) in Section 5.