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Izv. Akad. Nauk SSSR Ser. Mat., 1982, Volume 46, Issue 5, Pages 971–982 (Mi izv1654)  

This article is cited in 11 scientific papers (total in 11 papers)

Birational geometry of toric 3-folds

V. I. Danilov


Abstract: The following result is proved. Suppose given smooth toric $3$-folds $X$ and $Y$ and a proper birational toric morphism $f\colon X\to Y$. Then $f$ decomposes as a composite of blow-ups and blow-downs in smooth toric strata.
Bibliography: 7 titles.

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English version:
Mathematics of the USSR-Izvestiya, 1983, 21:2, 269–280

Bibliographic databases:

UDC: 513.6
MSC: Primary 14E30; Secondary 14E05, 14E35, 14M20
Received: 05.01.1982

Citation: V. I. Danilov, “Birational geometry of toric 3-folds”, Izv. Akad. Nauk SSSR Ser. Mat., 46:5 (1982), 971–982; Math. USSR-Izv., 21:2 (1983), 269–280

Citation in format AMSBIB
\Bibitem{Dan82}
\by V.~I.~Danilov
\paper Birational geometry of toric 3-folds
\jour Izv. Akad. Nauk SSSR Ser. Mat.
\yr 1982
\vol 46
\issue 5
\pages 971--982
\mathnet{http://mi.mathnet.ru/izv1654}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=675526}
\zmath{https://zbmath.org/?q=an:0536.14008}
\transl
\jour Math. USSR-Izv.
\yr 1983
\vol 21
\issue 2
\pages 269--280
\crossref{https://doi.org/10.1070/IM1983v021n02ABEH001790}


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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. G. Ewald, “Blow-ups of Smooth Toric 3-Varieties Werner Burau to his 80th birthday”, Abh Math Semin Univ Hambg, 57:1 (1987), 193  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. Udo Pachner, “P.L. Homeomorphic Manifolds are Equivalent by Elementary 5hellingst”, European Journal of Combinatorics, 12:2 (1991), 129  crossref
    4. Yu. G. Prokhorov, “On the existence of complements of the canonical divisor for Mori conic bundles”, Sb. Math., 188:11 (1997), 1665–1685  mathnet  crossref  crossref  mathscinet  zmath  isi
    5. I. V. Sobolev, “Action of Cyclic Groups on Fano 3-Folds”, Math. Notes, 68:5 (2000), 672–674  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
    6. I. Yu. Fedorov, “Blow-Ups of Three-Dimensional Terminal Singularities: The $cA$ Case”, Math. Notes, 71:3 (2002), 400–407  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
    7. I. Yu. Fedorov, “Divisorial contractions to 3-dimensional $cDV$ points”, Sb. Math., 193:7 (2002), 1091–1102  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
    8. Jarosław Włodarczyk, “Toroidal varieties and the weak factorization theorem”, Invent math, 154:2 (2003), 223  crossref  isi  elib
    9. V. Batyrev, F. Haddad, “On the Geometry of $\operatorname{SL}(2)$-Equivariant Flips”, Mosc. Math. J., 8:4 (2008), 621–646  mathnet  mathscinet  zmath
    10. DANIELE MUNDICI, “Invariant Measure Under the Affine Group Over”, Combinator. Probab. Comp, 2014, 1  crossref
    11. Ahmadinezhad H., “On pliability of del Pezzo fibrations and Cox rings”, J. Reine Angew. Math., 723 (2017), 101–125  crossref  mathscinet  zmath  isi
  • Известия Академии наук СССР. Серия математическая Izvestiya: Mathematics
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