Cubic fourfolds containing highly singular hyperplane sections

TL;DR

This paper constructs specific divisors in the moduli space of cubic fourfolds, identifying smooth fourfolds with highly singular hyperplane sections and demonstrating they are distinct from known special divisors.

Contribution

It introduces five new irreducible divisors in the moduli space of cubic fourfolds associated with highly singular hyperplane sections, not coinciding with Noether-Lefschetz divisors.

Findings

Constructed five irreducible divisors in the moduli space.

Proved these divisors are not Noether-Lefschetz divisors.

Utilized computational methods by Addington-Auel.

Abstract

We construct five irreducible divisors in the moduli space of complex cubic fourfolds parametrising smooth cubic fourfolds that contain highly singular hyperplane sections. We prove that each is not a Noether-Lefschetz (or Hassett) divisor, utilising the computational method developed by Addington-Auel.