VSPs of cubic fourfolds and the Gorenstein locus of the Hilbert scheme of 14 points on A^6

Abstract

This paper is concerned with the geometry of the Gorenstein locus of the Hilbert scheme of $14$ points on ${\mathbb{A}}^6$. This scheme has two components: the smoothable one and an exceptional one. We prove that the latter is smooth and identify the intersection of components as a vector bundle over the Iliev-Ranestad divisor in the space of cubic fourfolds. The ninth secant variety of the triple Veronese reembedding lies inside the Iliev-Ranestad divisor. We point out that this secant variety is set-theoretically a codimension two complete intersection and discuss the degrees of its equations.

17 pages, first version, comments welcome!

References in corpus (3)

• Irreducibility of the Gorenstein loci of Hilbert schemes via ray families
• The structure of the inverse system of Gorenstein k-algebras
• Murphy's Law for Hilbert function strata in the Hilbert scheme of points