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Sbornik: Mathematics, 2012, Volume 203, Issue 7, Pages 923–949
DOI: https://doi.org/10.1070/SM2012v203n07ABEH004248 (Mi sm7876) 		 
This article is cited in 52 scientific papers (total in 52 papers)

Flag varieties, toric varieties, and suspensions: Three instances of infinite transitivity

Ivan Arzhantseva, M. G. Zaidenbergb, K. G. Kuyumzhiyanc

a M. V. Lomonosov Moscow State University, Faculty of Mechanics and Mathematics
b University of Grenoble 1 — Joseph Fourier
c Laboratory of algebraic geometry and its applications, Higher School of Economics, Moscow
English version PDF (519 kB) Citations (52)
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DOI: https://doi.org/10.1070/SM2012v203n07ABEH004248
Abstract: We say that a group $G$ acts infinitely transitively on a set $X$ if for every $m\in\mathbb N$ the induced diagonal action of $G$ is transitive on the cartesian $m$th power $X^m\setminus\Delta$ with the diagonals removed. We describe three classes of affine algebraic varieties such that their automorphism groups act infinitely transitively on their smooth loci. The first class consists of normal affine cones over flag varieties, the second of nondegenerate affine toric varieties, and the third of iterated suspensions over affine varieties with infinitely transitive automorphism groups.
Bibliography: 42 titles.
Keywords: affine algebraic variety, automorphism, infinite transitivity, derivation.
Received: 07.04.2011 and 24.01.2012
Russian version:
Matematicheskii Sbornik, 2012, Volume 203, Number 7, Pages 3–30
DOI: https://doi.org/10.4213/sm7876
Bibliographic databases:
Document Type: Article
UDC: 512.745
MSC: 14R20, 14L30
Language: English
Original paper language: Russian
Citation: Ivan Arzhantsev, M. G. Zaidenberg, K. G. Kuyumzhiyan, “Flag varieties, toric varieties, and suspensions: Three instances of infinite transitivity”, Mat. Sb., 203:7 (2012), 3–30; Sb. Math., 203:7 (2012), 923–949
Citation in format AMSBIB
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