Equivariant Topological Classification of the Fano Varieties of Real Four-Dimensional Cubics

The equivariant topological type of the Fano variety parametrizing the set of lines on a nonsingular real hypersurface of degree three in a five-dimensional projective space is calculated. In the investigation of this Fano variety, results and constructions of the paper by Finashin and Kharlamov on the rigid projective classification of real four-dimensional cubics are used. The construction of Hassett (from the paper devoted to special four-dimensional cubics) is also applied.