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2013 | 11 | 11 | 1863-1880
Tytuł artykułu

Quotients of an affine variety by an action of a torus

Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
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.
Wydawca
Czasopismo
Rocznik
Tom
11
Numer
11
Strony
1863-1880
Opis fizyczny
Daty
wydano
2013-11-01
online
2013-08-23
Twórcy
Bibliografia
  • [1] Alexeev V., Brion M., Moduli of affine schemes with reductive group action, J. Algebraic Geom., 2005, 14(1), 83–117 http://dx.doi.org/10.1090/S1056-3911-04-00377-7
  • [2] Altmann K., Hausen J., Polyhedral divisors and algebraic torus actions, Math. Ann., 2006, 334(3), 557–607 http://dx.doi.org/10.1007/s00208-005-0705-8
  • [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 http://dx.doi.org/10.1307/mmj/1163789912
  • [5] Bertin J., The punctual Hilbert scheme: an introduction, available at http://cel.archives-ouvertes.fr/cel-00437713/en/
  • [6] Brion M., Invariant Hilbert schemes, preprint available at http://arxiv.org/abs/1102.0198
  • [7] Chuvashova O.V., The main component of the toric Hilbert scheme, Tôhoku Math. J., 2008, 60(3), 365–382 http://dx.doi.org/10.2748/tmj/1223057734
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Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.doi-10_2478_s11533-013-0295-8
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