We prove that the orbit closure of the determinant is not normal. A similar result is obtained for the padded permanent (i.e., the permanent multiplied by a power of a linear form).
Cite this article
Shrawan Kumar, Geometry of orbits of permanents and determinants. Comment. Math. Helv. 88 (2013), no. 3, pp. 759–788DOI 10.4171/CMH/302