Wyniki wyszukiwania

Sortuj według:

Ogranicz wyniki do:

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

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.

Linear bounds for levels of stable rationality

100%

Bogomolov F., Böhning C., Graf von Bothmer H.-C.

Open Mathematics

2012

tom 10

nr 2

466-520

Let G be one of the groups SLn(ℂ), Sp2n (ℂ), SOm(ℂ), Om(ℂ), or G 2. For a generically free G-representation V, we say that N is a level of stable rationality for V/G if V/G × ℙN is rational. In this paper we improve known bounds for the levels of stable rationality for the quotients V/G. In particular, their growth as functions of the rank of the group is linear for G being one of the classical groups.

Ograniczanie wyników

2 Open Mathematics

1 Bogomolov F.

1 Böhning C.

1 Chuvashova O.

1 Graf von Bothmer H.-C.

1 Pechenkin N.

1 2013

1 2012

Wyniki wyszukiwania

Quotients of an affine variety by an action of a torus

Linear bounds for levels of stable rationality