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Izv. Akad. Nauk SSSR Ser. Mat., 1984, Volume 48, Issue 2, Pages 237–263 (Mi izv1445)  

This article is cited in 19 scientific papers (total in 19 papers)

Toroidal Fano varieties and root systems

V. E. Voskresenskii, A. A. Klyachko


Abstract: In this paper it is shown that over an algebraically closed field there exist only finitely many mutually nonisomorphic toroidal Fano varieties. We give a complete description of toroidal Fano varieties with a centrally symmetric fan. We prove the rationality of a special class of toroidal Fano varieties and consider applications to problems of rationality of algebraic groups.
Bibliography: 17 titles.

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English version:
Mathematics of the USSR-Izvestiya, 1985, 24:2, 221–244

Bibliographic databases:

UDC: 512.7
MSC: Primary 14J40, 14L30; Secondary 14M20, 17B20
Received: 01.10.1982
Revised: 08.02.1983

Citation: V. E. Voskresenskii, A. A. Klyachko, “Toroidal Fano varieties and root systems”, Izv. Akad. Nauk SSSR Ser. Mat., 48:2 (1984), 237–263; Math. USSR-Izv., 24:2 (1985), 221–244

Citation in format AMSBIB
\Bibitem{VosKly84}
\by V.~E.~Voskresenskii, A.~A.~Klyachko
\paper Toroidal Fano varieties and root systems
\jour Izv. Akad. Nauk SSSR Ser. Mat.
\yr 1984
\vol 48
\issue 2
\pages 237--263
\mathnet{http://mi.mathnet.ru/izv1445}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=740791}
\zmath{https://zbmath.org/?q=an:0572.14029}
\transl
\jour Math. USSR-Izv.
\yr 1985
\vol 24
\issue 2
\pages 221--244
\crossref{https://doi.org/10.1070/IM1985v024n02ABEH001229}


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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. A. A. Klyachko, “Orbits of a maximal torus on a flag space”, Funct. Anal. Appl., 19:1 (1985), 65–66  mathnet  crossref  mathscinet  zmath  isi
    2. Yu. I. Manin, M. A. Tsfasman, “Rational varieties: algebra, geometry and arithmetic”, Russian Math. Surveys, 41:2 (1986), 51–116  mathnet  crossref  mathscinet  zmath  adsnasa  isi
    3. Peter Kleinschmidt, “A classification of toric varieties with few generators”, Aequ math, 35:2-3 (1988), 254  crossref  mathscinet  zmath
    4. Günter Ewald, “On the classification of toric fano varieties”, Discrete Comput Geom, 3:1 (1988), 49  crossref
    5. A. A. Borisov, L. A. Borisov, “Singular toric Fano varieties”, Russian Acad. Sci. Sb. Math., 75:1 (1993), 277–283  mathnet  crossref  mathscinet  zmath  adsnasa  isi
    6. V. I. Chernousov, “The group of congruence coefficients of a canonical quadratic form and stable rationality of the $PSO$ variety”, Math. Notes, 55:4 (1994), 413–416  mathnet  crossref  mathscinet  zmath  isi
    7. A. S. Merkurjev, “R-equivalence and rationality problem for semisimple adjoint classical algebraic groups”, Publications Mathématiques de l’Institut des Hautes Études Scientifiques, 84:1 (1996), 189  crossref  mathscinet  zmath
    8. NguyêñQuôć Thăńg, “On weak approximation in algebraic groups and related varieties defined by systems of forms”, Journal of Pure and Applied Algebra, 113:1 (1996), 67  crossref
    9. Philippe Gille, “La R-équivalence sur les groupes algébriques réductifs définis sur un corps global”, Publications Mathématiques de l’Institut des Hautes Études Scientifiques, 86:1 (1997), 199  crossref  mathscinet  zmath
    10. NGUYÊÑ QUÔĆ THǍŃG, “ON THE RATIONALITY OF ALMOST SIMPLE ALGEBRAIC GROUPS”, Int. J. Math, 10:05 (1999), 643  crossref
    11. V. V. Batyrev, “On the classification of toric Fano 4-folds”, J Math Sci, 94:1 (1999), 1021  crossref
    12. Anne Cortella, Boris Kunyavskiǐ, “Rationality Problem for Generic Tori in Simple Groups”, Journal of Algebra, 225:2 (2000), 771  crossref
    13. Hiroshi SATO, “Studies on toric Fano varieties”, Tohoku Math Publ, 23:23 (2002), 1  crossref  mathscinet
    14. Mikkel Øbro, “Classification of terminal simplicial reflexive d-polytopes with 3d − 1 vertices”, manuscripta math, 125:1 (2007), 69  crossref  mathscinet  isi
    15. Alan Stapledon, “Equivariant Ehrhart theory”, Advances in Mathematics, 226:4 (2011), 3622  crossref
    16. Giulio Cotignoli, Alexandru Sterian, “Existence of Indecomposable Rank Two Vector Bundles on Higher Dimensional Toric Varieties”, Communications in Algebra, 41:7 (2013), 2564  crossref
    17. J. Math. Sci. (N. Y.), 199:3 (2014), 302–305  mathnet  crossref
    18. Tristram Bogart, Milena Hering, Benjamin Nill, Günter Rote, Hal Schenck, “Finitely many smooth d-polytopes with n lattice points”, Isr. J. Math, 2015  crossref
    19. Xie F., “Toric Surfaces Over An Arbitrary Field Feild”, Pac. J. Math., 296:2 (2018), 481–507  crossref  isi
  • Известия Академии наук СССР. Серия математическая Izvestiya: Mathematics
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