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Izv. Akad. Nauk SSSR Ser. Mat., 1981, Volume 45, Issue 4, Pages 704–717 (Mi izv1581)  

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

Toroidal Fano 3-folds

V. V. Batyrev


Abstract: In this paper a regular classification of smooth Fano 3-folds is given.
Bibliography: 4 titles.

Full text: PDF file (1533 kB)
References: PDF file   HTML file

English version:
Mathematics of the USSR-Izvestiya, 1982, 19:1, 13–25

Bibliographic databases:

UDC: 513.6
MSC: Primary 14J30; Secondary 14N99
Received: 26.01.1981

Citation: V. V. Batyrev, “Toroidal Fano 3-folds”, Izv. Akad. Nauk SSSR Ser. Mat., 45:4 (1981), 704–717; Math. USSR-Izv., 19:1 (1982), 13–25

Citation in format AMSBIB
\Bibitem{Bat81}
\by V.~V.~Batyrev
\paper Toroidal Fano 3-folds
\jour Izv. Akad. Nauk SSSR Ser. Mat.
\yr 1981
\vol 45
\issue 4
\pages 704--717
\mathnet{http://mi.mathnet.ru/izv1581}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=631434}
\zmath{https://zbmath.org/?q=an:0495.14027|0478.14032}
\transl
\jour Math. USSR-Izv.
\yr 1982
\vol 19
\issue 1
\pages 13--25
\crossref{https://doi.org/10.1070/IM1982v019n01ABEH001404}


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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. V. E. Voskresenskii, A. A. Klyachko, “Toroidal Fano varieties and root systems”, Math. USSR-Izv., 24:2 (1985), 221–244  mathnet  crossref  mathscinet  zmath
    2. Peter Kleinschmidt, “A classification of toric varieties with few generators”, Aequ math, 35:2-3 (1988), 254  crossref  mathscinet  zmath
    3. Jörg Gretenkort, Peter Kleinschmidt, Bernd Sturmfels, “On the existence of certain smooth toric varieties”, Discrete Comput Geom, 5:1 (1990), 255  crossref  mathscinet  zmath
    4. 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
    5. A Klemm, B Lian, S.-S Roan, S.-T Yau, “Calabi-Yau four-folds for M- and F-theory compactifications”, Nuclear Physics B, 518:3 (1998), 515  crossref
    6. V. V. Batyrev, “On the classification of toric Fano 4-folds”, Journal of Mathematical Sciences (New York), 94:1 (1999), 1021  crossref  mathscinet  zmath
    7. C Casagrande, “Sur la géométrie birationnelle des variétés toriques de Fano de dimension 4”, Comptes Rendus de l'Académie des Sciences - Series I - Mathematics, 332:12 (2001), 1093  crossref
    8. Mikkel Øbro, “Classification of terminal simplicial reflexive d-polytopes with 3d − 1 vertices”, manuscripta math, 125:1 (2007), 69  crossref  mathscinet  isi
    9. Edilaine Ervilha Nobili, “Classification of Toric 2-Fano 4-folds”, Bull Braz Math Soc, New Series, 42:3 (2011), 399  crossref
    10. John Davey, Amihay Hanany, Noppadol Mekareeya, Giuseppe Torri, “M2-branes and Fano 3-folds”, J. Phys. A: Math. Theor, 44:40 (2011), 405401  crossref
    11. Prabwal Phukon, Tapobrata Sarkar, “On the Higgsing and UnHiggsing of Fano 3-folds”, J. High Energ. Phys, 2012:1 (2012)  crossref
    12. A. Hanany, R.-K. Seong, “Brane tilings and reflexive polygons”, Fortschr. Phys, 2012, n/a  crossref
    13. Hiroshi Sato, “The Numerical Class of a Surface on a Toric Manifold”, International Journal of Mathematics and Mathematical Sciences, 2012 (2012), 1  crossref
    14. Gloria Della Noce, “A note on the Picard number of singular Fano 3-folds”, Geom Dedicata, 2013  crossref
    15. Xinhong Chen, Ming Lu, “Coxeter transformations of the derived categories of coherent sheaves”, Journal of Algebra, 399 (2014), 79  crossref
    16. Makiko Mase, “Families of K3 Surfaces in Smooth Fano 3-Folds with Picard Number 2”, Viet J Math, 2014  crossref
    17. Hokuto Uehara, “Exceptional collections on toric Fano threefolds and birational geometry”, Int. J. Math, 25:07 (2014), 1450072  crossref
    18. Ryo Kawaguchi, “The lower bound for the volume of a three-dimensional convex polytope”, Algebra Discrete Math., 20:2 (2015), 263–285  mathnet  mathscinet
    19. V. V. Przyjalkowski, I. A. Cheltsov, K. A. Shramov, “Fano threefolds with infinite automorphism groups”, Izv. Math., 83:4 (2019), 860–907  mathnet  crossref  crossref  mathscinet  adsnasa  isi  elib
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