On cubic fourfolds with an inductive structure

TL;DR

This paper investigates the geometric structure of certain cubic fourfolds with an inductive property, analyzing their planes and determining their transcendental lattices to understand their complex structure.

Contribution

It introduces a new class of cubic fourfolds with inductive structures and computes their transcendental lattices, advancing understanding of their geometric and algebraic properties.

Findings

Determined the number of planes on these cubic fourfolds.

Computed the transcendental lattices for this class of fourfolds.

Identified structural properties related to their inductive nature.

Abstract

We study the number of planes for four dimensional projective hypersurfaces which has so-called inductive structure. We also determine transcendental lattices for cubic fourfolds of this type.