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Quotients of an affine variety by an action of a torus

100%
Chuvashova O., Pechenkin N.
Open Mathematics
|
2013
|
tom 11
|
nr 11
1863-1880
EN
Let X be an affine T-variety. We study two different quotients for the action of T on X: the toric Chow quotient X/C T and the toric Hilbert scheme H. We introduce a notion of the main component H 0 of H, which parameterizes general T-orbit closures in X and their flat limits. The main component U 0 of the universal family U over H is a preimage of H 0. We define an analogue of a universal family WX over the main component of X/C T. We show that the toric Chow morphism restricted on the main components lifts to a birational projective morphism from U 0 to W X. The variety W X also provides a geometric realization of the Altmann-Hausen family. In particular, the notion of W X allows us to provide an explicit description of the fan of the Altmann-Hausen family in the toric case.
2
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Three-dimensional terminal toric flips

100%
Fujino O., Sato H., Takano Y., Uehara H.
Open Mathematics
|
2009
|
tom 7
|
nr 1
46-53
EN
We describe three-dimensional terminal toric flips. We obtain the complete local description of three-dimensional terminal toric flips.
3
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On orbits of the automorphism group on an affine toric variety

88%
Arzhantsev I., Bazhov I.
Open Mathematics
|
2013
|
tom 11
|
nr 10
1713-1724
EN
Let X be an affine toric variety. The total coordinates on X provide a canonical presentation $$\bar X \to X$$ of X as a quotient of a vector space $$\bar X$$ by a linear action of a quasitorus. We prove that the orbits of the connected component of the automorphism group Aut(X) on X coincide with the Luna strata defined by the canonical quotient presentation.
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