On affine real cubic surfaces (Q6592301)

The authors classify smooth real spatial cubic surfaces in the presence of a smooth hyperplane section (affine cubics in short) up to equivariant deformation in the class of such surfaces. They find that there are \(15\) deformation classes (vs.\ Schläfli's five classes of projective cubics) and, in most cases, these classes can be distinguished by the homeomorphism type of the real part of the affine part of the surface. In the one exceptional case, one has to appeal to the projectivization and evaluate the so-called Rokhlin-Guillou-Marin form on the oval of the section. (It appears that, in order to tell this ``oval'' apart, one also has to consider the section as a two-component cubic curve on the cutting plane.)