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arXiv:math/0603703 [math.AG]AbstractReferencesReviewsResources

The main component of the toric Hilbert scheme

O. V. Chuvashova

Published 2006-03-30, updated 2008-02-24Version 3

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.

Comments: 18 pages
Categories: math.AG, math.RT
Subjects: 14C05, 52B20, 14M25
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