| The multigraded Hilbert schemes have been introduced by Haiman and Sturmfels. They are a generalization of the usual Hilbert schemes and parametrize homogeneous ideals in a graded polynomial ring. In this talk, I will concentrate on graded Hilbert schemes parametrizing quasi-homogeneous ideals in k[x,y]. I will report some results about their irreducibility and their Chow ring. |