27 lines on singular cubic surfaces
A famous result of classical algebraic geometry states that every smooth cubic surface contains precisely 27 lines. The subspace of the Grassmannian parameterizing these lines is called the Fano variety of lines of the cubic surface. In this talk I will at first present some general facts about the Fano variety of lines for smooth cubic hypersurfaces. Afterwards I will discuss the case of cubic hypersurfaces admitting a unique singular point and, in the end, explain what happens to the 27 lines on a cubic surface in this case.