Grothendieck ring of varieties and cubic hypersurfaces

Let Y be a cubic hypersurface. In the paper arxiv/1405.5154 [GS14] Galkin and Shinder derived a Y-F(Y) relation. This relation expresses Y in terms of the hilbert schemes of two points on Y and variety F(Y) of lines on Y in the Grothendieck ring of varieties K_0(Var/k). In this talk we recall basic facts about the Grothendieck ring of varieties and derive the Y-F(Y) relation. And discuss possible generalizations to the hilbert scheme of four points on Y. Most part of the talk will follow [GS14]. [GS14] Sergey Galkin, Evgeny Shinder, The Fano variety of lines and rationality problem for a cubic hypersurface.