On orbits of the automorphism group on an affine toric variety

• Autorzy: Ivan Arzhantsev , Ivan Bazhov
• Języki publikacji: EN

Abstrakty

EN

Let X be an affine toric variety. The total coordinates on X provide a canonical presentation $$\bar X \to X$$ of X as a quotient of a vector space $$\bar X$$ by a linear action of a quasitorus. We prove that the orbits of the connected component of the automorphism group Aut(X) on X coincide with the Luna strata defined by the canonical quotient presentation.

Słowa kluczowe

EN

Toric variety; Cox ring; Automorphism; Quotient; Luna stratification

Kategorie tematyczne

• 14R20: Group actions on affine varieties
• 14J50: Automorphisms of surfaces and higher-dimensional varieties
• 14L30: Group actions on varieties or schemes (quotients)
• 14M25: Toric varieties, Newton polyhedra

• Wydawca: De Gruyter Open
• Czasopismo: Open Mathematics
• Rocznik: 2013
• Tom: 11
• Numer: 10
• Strony: 1713-1724

Daty

wydano

2013-10-01

online

2013-07-20

Twórcy

autor

Ivan Arzhantsev

autor

Ivan Bazhov

• Department of Higher Algebra, Faculty of Mechanics and Mathematics, Lomonosov Moscow State University, Leninskie Gory 1, GSP-1, Moscow, 119991, Russia

Bibliografia

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• [2] Arzhantsev I.V., Derenthal U., Hausen J., Laface A., Cox rings, preprint available at http://arxiv.org/abs/1003.4229
• [3] Arzhantsev I.V., Flenner H., Kaliman S., Kutzschebauch F., Zaidenberg M., Flexible varieties and automorphism groups, Duke Math. J., 2013, 162(4), 767–823 http://dx.doi.org/10.1215/00127094-2080132[Crossref][WoS]
• [4] Arzhantsev I.V., Kuyumzhiyan K., Zaidenberg M., Flag varieties, toric varieties, and suspensions: three examples of infinite transitivity, Sb. Math., 2012, 203(7–8), 923–949 http://dx.doi.org/10.1070/SM2012v203n07ABEH004248[WoS][Crossref]
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Identyfikatory

DOI

10.2478/s11533-013-0273-1