Quotients of an affine variety by an action of a torus

• Autorzy: Olga Chuvashova , Nikolay Pechenkin
• 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.

Słowa kluczowe

EN

Torus action; Toric variety; Toric Chow quotient; Toric Hilbert scheme

Kategorie tematyczne

• 14L24: Geometric invariant theory
• 14C05: Parametrization (Chow and Hilbert schemes)
• 14M25: Toric varieties, Newton polyhedra

• Wydawca: De Gruyter Open
• Czasopismo: Open Mathematics
• Rocznik: 2013
• Tom: 11
• Numer: 11
• Strony: 1863-1880

Daty

wydano

2013-11-01

online

2013-08-23

Twórcy

autor

Olga Chuvashova

• Moscow State University

autor

Nikolay Pechenkin

• Steklov Mathematical Institute

Bibliografia

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Identyfikatory

DOI

10.2478/s11533-013-0295-8