THE MAIN COMPONENT OF THE TORIC HILBERT SCHEME

摘要

Let X be an affine toric variety with big torus T subset of X and let T subset of T be a subtorus. The general T-orbit Closures in X and their flat limits are parametrized by the main component H-0 of the toric Hilbert scheme. Further. the quotient torus T/T acts on H-0 with a dense orbit. We describe the fan of this toric variety: this leads us to an integral analogue Of the fiber polytope of Billera and Sturmfels. We also describe the relation of H-0 to the main component of the inverse limit of GIT quotients of X by T.