Graphs of schemes associated to group actions

Let X be a proper algebraic scheme over an algebraically closed field. We assume that a torus T acts on X such that the action has isolated fixed points. The T -graph of X can be defined using the fixed points and the one-dimensional orbits of the T -action. If the upper Borel subgroup of the general linear group with maximal torus T acts on X, then we can define a second graph associated to X, called the A -graph of X. We prove that the A -graph of X is connected if and only if X is connected. We use this result to give proof of Hartshorne's theorem on the connectedness of the Hilbert scheme in the case of d points in Pn.