Towards an equivariant Bézout's theorem

Bézout’s theorem is a fundamental result in enumerative geometry which can be used to compute the degree of the intersection of a finite number of varieties in general position. In its simplest formulation it can be used to predict the number of points of intersection of n hypersurfaces in P^n, which, when counted appropriately, is given by the product of the degrees of the defining polynomials. The goal of this talk, based on a joint work with S. Costenoble and S. Tilson, is to illustrate how to generalise this classical result and its proof to the case of varieties endowed with an action of Z/2. The solution to this problem crucially relies on the computation for projective spaces of a generalisation due to Costenoble-Waner of Bredon equivariant cohomology.