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arXiv · 2605.09531

The equations of general Hassett maximal cubic fourfolds

Elad Gal·Howard Nuer
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Abstract

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.

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Elad Gal, Howard Nuer. 2026-05-10. The equations of general Hassett maximal cubic fourfolds. https://arxiv.org/abs/2605.09531

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