VSPs of cubic fourfolds and the Gorenstein locus of the Hilbert scheme of 14 points on A⁶

2016/11/14 by Joachim Jelisiejew, Jelisiejew, Joachim
Mathematics · #13H10 #14C05 (primary) #14J70 (secondary) #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Commutative Algebra and Its Applications #FOS: Mathematics #Tensor decomposition and applications

paper · pdf · doi:10.48550/arxiv.1611.04345

openalex publication_date 2016/11/14 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

This paper is concerned with the geometry of the Gorenstein locus of the Hilbert scheme of 14 points on \mathbbA⁶. 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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• K3-surfaces of genus 8 and varieties of sums of powers of cubic fourfolds
• Smoothable zero dimensional schemes and special projections of algebraic varieties
• Variety of power sums and divisors in the moduli space of cubic fourfolds
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