The main component of the toric Hilbert scheme

2006/03/30 by Chuvashova, O. V.
#14C05 (Primary) #14M25 (Secondary) #52B20 #Algebraic Geometry (math.AG) #FOS: Mathematics #Representation Theory (math.RT)

paper · doi:10.48550/arxiv.math/0603703

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 H₀ of the toric Hilbert scheme. Further, the quotient torus \T/T acts on H₀ 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 H₀ to the main component of the inverse limit of GIT quotients of \X by T.

Related

• Fiber fans and toric quotients
• Toric Varieties in Hilbert Schemes
• Non-coherent Components of the Toric Hilbert Scheme
• The moduli stack of affine stable toric varieties
• The Chow ring of punctual Hilbert schemes of toric surfaces