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Open Mathematics

formerly Central European Journal of Mathematics

Editor-in-Chief: Gianazza, Ugo / Vespri, Vincenzo

1 Issue per year


IMPACT FACTOR 2016 (Open Mathematics): 0.682
IMPACT FACTOR 2016 (Central European Journal of Mathematics): 0.489

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ISSN
2391-5455
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Volume 11, Issue 10 (Oct 2013)

Issues

On orbits of the automorphism group on an affine toric variety

Ivan Arzhantsev
  • Department of Higher Algebra, Faculty of Mechanics and Mathematics, Lomonosov Moscow State University, Leninskie Gory 1, GSP-1, Moscow, 119991, Russia
  • School of Applied Mathematics and Information Science, National Research University Higher School of Economics, Pokrovskiy Boulevard 11, Moscow, 109028, Russia
  • Email:
/ Ivan Bazhov
  • Department of Higher Algebra, Faculty of Mechanics and Mathematics, Lomonosov Moscow State University, Leninskie Gory 1, GSP-1, Moscow, 119991, Russia
  • Email:
Published Online: 2013-07-20 | DOI: https://doi.org/10.2478/s11533-013-0273-1

Abstract

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.

MSC: 14M25; 14R20; 14J50; 14L30

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

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About the article

Published Online: 2013-07-20

Published in Print: 2013-10-01


Citation Information: Open Mathematics, ISSN (Online) 2391-5455, DOI: https://doi.org/10.2478/s11533-013-0273-1.

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© 2013 Versita Warsaw. This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License. BY-NC-ND 3.0

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