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

Joachim Jelisiejew

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arXiv · 1611.04345

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

Joachim Jelisiejew

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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.

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BibTeX RIS

Joachim Jelisiejew. 2016-11-14. VSPs of cubic fourfolds and the Gorenstein locus of the Hilbert scheme of 14 points on A^6. https://arxiv.org/abs/1611.04345

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