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2008 The main component of the toric Hilbert scheme
Olga V. Chuvashova
Tohoku Math. J. (2) 60(3): 365-382 (2008). DOI: 10.2748/tmj/1223057734


Let $\boldsymbol{X}$ be an affine toric variety with big torus $\boldsymbol{T}\subset \boldsymbol{X}$ and let $T\subset\boldsymbol{T}$ be a subtorus. The general $T$-orbit closures in $\boldsymbol{X}$ and their flat limits are parametrized by the main component $H_0$ of the toric Hilbert scheme. Further, the quotient torus $\boldsymbol{T}/T$ 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 $\boldsymbol{X}$ by $T$.


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Olga V. Chuvashova. "The main component of the toric Hilbert scheme." Tohoku Math. J. (2) 60 (3) 365 - 382, 2008.


Published: 2008
First available in Project Euclid: 3 October 2008

zbMATH: 1160.14001
MathSciNet: MR2453729
Digital Object Identifier: 10.2748/tmj/1223057734

Primary: 14C05
Secondary: 14M25 , 52B20

Keywords: fiber polytope , toric Chow quotient , Toric Hilbert scheme

Rights: Copyright © 2008 Tohoku University


Vol.60 • No. 3 • 2008
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