English

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

R2 v1 2026-07-22T17:33:31.380Z