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Mat. Sb., 2004, Volume 195, Number 6, Pages 3–20 (Mi msb819)  

This article is cited in 4 scientific papers (total in 4 papers)

Classification of affine homogeneous spaces of complexity one

I. V. Arzhantsev, O. V. Chuvashova

M. V. Lomonosov Moscow State University

Abstract: The complexity of an action of a reductive algebraic group $G$ on an algebraic variety $X$ is the codimension of a generic $B$-orbit in $X$, where $B$ is a Borel subgroup of $G$. Affine homogeneous spaces $G/H$ of complexity 1 are classified in this paper. These results are the natural continuation of the earlier classification of spherical affine homogeneous spaces, that is, spaces of complexity 0.

DOI: https://doi.org/10.4213/sm819

Full text: PDF file (332 kB)
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English version:
Sbornik: Mathematics, 2004, 195:6, 765–782

Bibliographic databases:

UDC: 512.745
MSC: Primary 14M17, 14R20, 37J35; Secondary 22F30, 32M10, 53C30
Received: 06.03.2003 and 12.01.2004

Citation: I. V. Arzhantsev, O. V. Chuvashova, “Classification of affine homogeneous spaces of complexity one”, Mat. Sb., 195:6 (2004), 3–20; Sb. Math., 195:6 (2004), 765–782

Citation in format AMSBIB
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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. Mykytyuk I., Panasyuk A., “Bi-Poisson Structures and Integrability of Geodesic Flow on Homogeneous Spaces”, Transform. Groups, 9:3 (2004), 289–308  crossref  mathscinet  zmath  isi
    2. I. V. Losev, “Calculating Cartan spaces for affine homogeneous spaces”, Sb. Math., 198:10 (2007), 1407–1431  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
    3. Jovanovic B., “Geodesic Flows on Riemannian g.o. Spaces”, Regular & Chaotic Dynamics, 16:5 (2011), 504–513  crossref  mathscinet  zmath  adsnasa  isi
    4. Langlois K., Terpereau R., “on the Geometry of Normal Horospherical G-Varieties of Complexity One”, J. Lie Theory, 26:1 (2016), 49–78  mathscinet  zmath  isi
  • Математический сборник - 1992–2005 Sbornik: Mathematics (from 1967)
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