The topological classification of Fano surfaces of real three-dimensional cubics

We consider surfaces whose points are the lines on the real three-dimensional varieties of degree 3. These surfaces are called Fano surfaces. This paper deals with finding the topological types, that is, a topological classification, of real Fano surfaces. Moreover, we prove that the equivariant topological type of the corresponding complex Fano surface with the involution of complex conjugation determines the rigid isotopy class of the corresponding real three-dimensional cubic.