A nonspecial divisor in the moduli space of cubic fourfolds via 10-nodal plane sextics

TL;DR

This paper identifies a special irreducible divisor in the moduli space of cubic fourfolds characterized by a 10-nodal plane sextic discriminant, expanding understanding of geometric conditions beyond classical Noether-Lefschetz divisors.

Contribution

It introduces a new geometric divisor in the moduli space of cubic fourfolds defined by a 10-nodal plane sextic, not of Noether-Lefschetz type.

Findings

The divisor is irreducible in the moduli space.

It is characterized by a net of polar quadrics with a 10-nodal sextic discriminant.

The divisor is distinct from classical Noether-Lefschetz divisors.

Abstract

In the moduli space $\mathcal{C}$ of complex cubic hypersurfaces $X\subset\mathbb{P}^5$, we study the condition that $X$ admits a net of polar quadrics whose discriminant locus is a $10$-nodal irreducible plane sextic curve. Our main result is that such a condition defines an irreducible divisor in $\mathcal{C}$ which is not of Noether-Lefschetz type.