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Mat. Sb., 1992, Volume 183, Number 2, Pages 134–141 (Mi msb1470)  

This article is cited in 18 scientific papers (total in 18 papers)

Singular toric Fano varieties

A. A. Borisov, L. A. Borisov

M. V. Lomonosov Moscow State University

Abstract: The authors prove that the number of types of toric Fano varieties with certain constraints on the singularities is finite.

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English version:
Russian Academy of Sciences. Sbornik. Mathematics, 1993, 75:1, 277–283

Bibliographic databases:

MSC: 14J45, 14M25
Received: 25.09.1990

Citation: A. A. Borisov, L. A. Borisov, “Singular toric Fano varieties”, Mat. Sb., 183:2 (1992), 134–141; Russian Acad. Sci. Sb. Math., 75:1 (1993), 277–283

Citation in format AMSBIB
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\by A.~A.~Borisov, L.~A.~Borisov
\paper Singular toric Fano varieties
\jour Mat. Sb.
\yr 1992
\vol 183
\issue 2
\pages 134--141
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\transl
\jour Russian Acad. Sci. Sb. Math.
\yr 1993
\vol 75
\issue 1
\pages 277--283
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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. Alexandr Borisov, “Minimal discrepancies of toric singularities”, manuscripta math, 92:1 (1997), 33  crossref  mathscinet  zmath  isi
    2. Kreuzer M., Skarke H., “On the Classification of Reflexive Polyhedra”, Commun. Math. Phys., 185:2 (1997), 495–508  crossref  mathscinet  zmath  adsnasa  isi
    3. V. V. Batyrev, “On the classification of toric Fano 4-folds”, Journal of Mathematical Sciences (New York), 94:1 (1999), 1021  crossref  mathscinet  zmath
    4. Yu. G. Prokhorov, V. V. Shokurov, “The first main theorem on complements: from global to local”, Izv. Math., 65:6 (2001), 1169–1196  mathnet  crossref  crossref  mathscinet  zmath  elib
    5. Proc. Steklov Inst. Math., 240 (2003), 75–213  mathnet  mathscinet  zmath
    6. Debarre O., “Fano Varieties”, Higher Dimensional Varieties and Rational Points, Bolyai Society Mathematical Studies, 12, eds. Boroczky K., Kollar K., Szamuely T., Springer-Verlag Berlin, 2003, 93–132  mathscinet  isi
    7. McKernan, J, “Threefold thresholds”, Manuscripta Mathematica, 114:3 (2004), 281  crossref  mathscinet  zmath  isi  elib
    8. K. A. Shramov, “Elementary Birational Maps between Mori Toric Fiber 3-Spaces”, Math. Notes, 78:1 (2005), 120–127  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
    9. Nill, B, “Volume and lattice points of reflexive simplices”, Discrete & Computational Geometry, 37:2 (2007), 301  crossref  mathscinet  zmath  isi
    10. Pasquier B., “Fano Horospherical Varieties”, Bull. Soc. Math. Fr., 136:2 (2008), 195–225  mathscinet  zmath  isi
    11. Okada T., “On the Birational Unboundedness of Higher Dimensional Q-Fano Varieties”, Math. Ann., 345:1 (2009), 195–212  crossref  mathscinet  zmath  isi
    12. Prokhorov Yu.G., Shokurov V.V., “Towards the Second Main Theorem on Complements”, J. Algebr. Geom., 18:1 (2009), 151–199  crossref  mathscinet  zmath  isi  elib
    13. Prokhorov Yu., “Q-Fano Threefolds of Large Fano Index, I”, Doc Math, 15 (2010), 843–872  isi
    14. Kasprzyk A.M., “Canonical Toric Fano Threefolds”, Can. J. Math.-J. Can. Math., 62:6 (2010), 1293–1309  crossref  isi
    15. Averkov G., “On the Size of Lattice Simplices with a Single Interior Lattice Point”, SIAM Discret. Math., 26:2 (2012), 515–526  crossref  mathscinet  zmath  isi
    16. Coates T., Gonshaw S., Kasprzyk A., Nabijou N., “Mutations of Fake Weighted Projective Spaces”, Electron. J. Comb., 21:4 (2014)  isi
    17. B. Bechtold, J. Hausen, E. Huggenberger, M. Nicolussi, “On Terminal Fano 3-Folds with 2-Torus Action”, International Mathematics Research Notices, 2015  crossref
    18. Jiang Ch., “On Birational Boundedness of Fano Fibrations”, Am. J. Math., 140:5 (2018), 1253–1276  crossref  zmath  isi  scopus
  • Математический сборник - 1992–2005 Sbornik: Mathematics (from 1967)
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