Topology of real cubic fourfolds

TL;DR

This paper provides a topological classification of real cubic fourfolds, showing how their real loci can be constructed from a projective 4-space through handle additions or spherical components.

Contribution

It offers a complete topological classification of real cubic fourfolds, detailing how their real loci are formed from basic topological operations.

Findings

Real cubic fourfolds' real loci are obtained by handle additions or spherical components.

Classification covers all non-singular real cubic fourfolds.

Provides a constructive topological description of real loci.

Abstract

A solution to the problem of topological classification of real cubic fourfolds is presented. It is shown that the real locus of a real non-singular cubic fourfold is obtained from a projective 4-space either by adding several trivial one- and two-handles, or by adding a spherical connected component.