About Hessian varieties of cubic hypersurfaces

[...] In this talk, I will present some joint results with G. P. Pirola and D. Bricalli about the geometry of Hessian varieties of cubic hypersurfaces. In particular, we will describe the singular locus of the Hessian variety of a general cubic fourfold, and we will discuss the characterisation of smooth cubic threefolds and fourfolds whose Hessian variety is reducible. If time permits, I will also mention a recent related work in progress.