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The main component of the toric Hilbert scheme

O. V. Chuvashova
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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.

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O. V. Chuvashova. 2008-02-24. The main component of the toric Hilbert scheme. https://arxiv.org/abs/math/0603703

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