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Quotients of an affine variety by an action of a torus

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Chuvashova O., Pechenkin N.

Open Mathematics

2013

tom 11

nr 11

1863-1880

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.

Ograniczanie wyników

1 Open Mathematics

1 Chuvashova O.

1 Pechenkin N.

1 2013

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Quotients of an affine variety by an action of a torus