Author:
Chuvashova Olga,Pechenkin Nikolay
Abstract
AbstractLet 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.
Reference21 articles.
1. Alexeev V., Brion M., Moduli of affine schemes with reductive group action, J. Algebraic Geom., 2005, 14(1), 83–117
2. Altmann K., Hausen J., Polyhedral divisors and algebraic torus actions, Math. Ann., 2006, 334(3), 557–607
3. Arzhantsev I.V., Hausen J., On the multiplication map of a multigraded algebra, Math. Res. Lett., 2007, 14(1), 129–136
4. Berchtold F., Hausen J., GIT-equivalence beyond the ample cone, Michigan Math. J., 2006, 54(3), 483–515
5. Bertin J., The punctual Hilbert scheme: an introduction, available at http://cel.archives-ouvertes.fr/cel-00437713/en/
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