On Affine Real Cubic Surfaces

TL;DR

This paper classifies the 15 connected components of the space of non-singular real affine cubic surfaces, providing topological criteria and describing how these components are related through wall-crossing phenomena.

Contribution

It establishes a complete topological classification of affine real cubic surfaces and details their adjacency relations, advancing understanding of their geometric structure.

Findings

Identified 15 connected components of the space of non-singular real affine cubic surfaces.

Provided topological criteria to distinguish these components.

Described how the components are connected via wall-crossing.

Abstract

We prove that the space of affine, transversal at infinity, non-singular real cubic surfaces has 15 connected components. We give a topological criterion to distinguish them and show also how these 15 components are adjacent to each other via wall-crossing.