The main component of the toric Hilbert scheme
Algebraic Geometry
2008-02-25 v3 Representation Theory
Abstract
Let \X be an affine toric variety under a torus \T and let 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.
Keywords
Cite
@article{arxiv.math/0603703,
title = {The main component of the toric Hilbert scheme},
author = {O. V. Chuvashova},
journal= {arXiv preprint arXiv:math/0603703},
year = {2008}
}
Comments
18 pages