arXiv subjects

Elad Gal

Publications and source records attributed to Elad Gal.

2 recordsLinked to original sources

arXiv2026

The equations of general Hassett maximal cubic fourfolds

In this note, we discuss Hassett maximal cubic fourfolds and construct an explicit irreducible component of maximal dimension sixteen of the locus $\mathcal{Z}$ of Hassett maximal cubic fourfolds. We utilize algebraic and arithmetic methods to analyze the associated lattice of these fourfolds. % By studying general integral quadratic forms and proving the ADC property for a specific ternary form, we demonstrate that the primitive image of our lattice spans the entire Hassett subset, confirming the Hassett maximality of the cubic fourfolds we describe.

math.AG↗

arXiv2023

Supporting rank and the intersection of all Hassett Divisors

We prove that the dimension of the intersection $\mathcal Z$ of all Hassett divisors of special cubic fourfolds is sixteen. We do this by studying which subsets of the natural numbers $\mathbb N$ can be obtained as the image of a positive-definite integral quadratic form and what the minimal possible rank of such a form is. In particular, for the subset of $\mathbb N$ consisting of all possible discriminants of special cubic fourfolds, we show this rank is four and that this is the codimension of $\mathcal Z$ in $\mathcal C$, the twenty-dimensional moduli space of cubic fourfolds.

math.AG↗