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Izv. Akad. Nauk SSSR Ser. Mat., 1985, Volume 49, Issue 3, Pages 635–651 (Mi izv1368)  

This article is cited in 35 scientific papers (total in 35 papers)

The nonvanishing theorem

V. V. Shokurov


Abstract: The main result of the paper is a nonvanishing theorem that is a sufficient condition for nontriviality of the zeroth cohomology group of inverse sheaves. In addition, applications of this theorem to multidimensional projective geometry are indicated and problems illuminating further insight into the theory of Mori extremal rays are formulated.
Bibliography: 14 titles.

Full text: PDF file (1606 kB)
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English version:
Mathematics of the USSR-Izvestiya, 1986, 26:3, 591–604

Bibliographic databases:

UDC: 512.7
MSC: Primary 14J10; Secondary 14F12, 14E30, 14J30
Received: 28.09.1983

Citation: V. V. Shokurov, “The nonvanishing theorem”, Izv. Akad. Nauk SSSR Ser. Mat., 49:3 (1985), 635–651; Math. USSR-Izv., 26:3 (1986), 591–604

Citation in format AMSBIB
\Bibitem{Sho85}
\by V.~V.~Shokurov
\paper The nonvanishing theorem
\jour Izv. Akad. Nauk SSSR Ser. Mat.
\yr 1985
\vol 49
\issue 3
\pages 635--651
\mathnet{http://mi.mathnet.ru/izv1368}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=794958}
\zmath{https://zbmath.org/?q=an:0605.14006}
\transl
\jour Math. USSR-Izv.
\yr 1986
\vol 26
\issue 3
\pages 591--604
\crossref{https://doi.org/10.1070/IM1986v026n03ABEH001160}


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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. Mauro Beltrametti, “Alcuni risultati sulla classificazione delle varieta’ algebriche a piu’ dimensioni”, Seminario Mat e Fis di Milano, 57:1 (1987), 63  crossref  mathscinet  zmath
    2. V. V. Nikulin, “Del Pezzo surfaces with log-terminal singularities. II”, Math. USSR-Izv., 33:2 (1989), 355–372  mathnet  crossref  mathscinet  zmath
    3. V. V. Nikulin, “Del Pezzo surfaces with log-terminal singularities. III”, Math. USSR-Izv., 35:3 (1990), 657–675  mathnet  crossref  mathscinet  zmath
    4. V. V. Nikulin, “Del Pezzo surfaces with log-terminal singularities”, Math. USSR-Sb., 66:1 (1990), 231–248  mathnet  crossref  mathscinet  zmath  isi
    5. V. V. Nikulin, “Algebraic three-folds and the diagram method”, Math. USSR-Izv., 37:1 (1991), 157–189  mathnet  crossref  mathscinet  zmath  adsnasa
    6. Yujiro Kawamata, “Abundance theorem for minimal threefolds”, Invent math, 108:1 (1992), 229  crossref  mathscinet  zmath  isi
    7. Kollar J., “Flips and Abundance for Algebraic Threefolds - a Summer Seminar at the University-of-Utah (Salt-Lake-City, 1991) - Preface”, Asterisque, 1992, no. 211, 1+  mathscinet  isi
    8. M. L. Fania, “When K+(n-4)L fails to be nef”, manuscripta math, 79:1 (1993), 209  crossref  mathscinet  zmath  isi
    9. Russian Acad. Sci. Izv. Math., 42:2 (1994), 371–425  mathnet  crossref  mathscinet  zmath  adsnasa  isi
    10. Yu. G. Prokhorov, “The existence of a smooth divisor on Fano 4-folds of index 2”, Russian Acad. Sci. Sb. Math., 83:1 (1995), 119–131  mathnet  crossref  mathscinet  zmath  isi
    11. F. Ambro, “Ladders on Fano varieties”, J Math Sci, 94:1 (1999), 1126  crossref
    12. V. A. Iskovskikh, “Birational rigidity of Fano hypersurfaces in the framework of Mori theory”, Russian Math. Surveys, 56:2 (2001), 207–291  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
    13. V. A. Iskovskikh, “On Shokurov's Work Prelimiting Flips”, Proc. Steklov Inst. Math., 240 (2003), 16–36  mathnet  mathscinet  zmath
    14. Proc. Steklov Inst. Math., 240 (2003), 214–233  mathnet  mathscinet  zmath
    15. Proc. Steklov Inst. Math., 240 (2003), 75–213  mathnet  mathscinet  zmath
    16. V. V. Shokurov, “Letters of a Bi-rationalist V: Mld's and Termination of Log Flips”, Proc. Steklov Inst. Math., 246 (2004), 315–336  mathnet  mathscinet  zmath
    17. Yoshiaki Fukuma, “On the Sectional Geometric Genus of Quasi-Polarized Varieties. I”, Communications in Algebra, 32:3 (2004), 1069  crossref
    18. V. A. Iskovskikh, V. V. Shokurov, “Birational models and flips”, Russian Math. Surveys, 60:1 (2005), 27–94  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  elib
    19. Su Ji-hong, Zhao Yi-cai, “On structure of small contractions of odd dimensional projective varieties”, Sci China Ser A, 50:4 (2007), 495  crossref  mathscinet  zmath  isi
    20. Yoshiaki Fukuma, “On the dimension of global sections of adjoint bundles for polarized 3-folds and 4-folds”, Journal of Pure and Applied Algebra, 211:3 (2007), 609  crossref
    21. V. V. Shokurov, “Letters of a Bi-rationalist. VII Ordered Termination”, Proc. Steklov Inst. Math., 264 (2009), 178–200  mathnet  crossref  mathscinet  isi  elib  elib
    22. Druel S., “Existence of Minimal Models for General Type Varieties”, Asterisque, 2009, no. 326, 1–38  mathscinet  zmath  isi
    23. Caucher Birkar, “On existence of log minimal models”, Compositio Math, 2010, 1  crossref  isi
    24. Prokhorov Yu., “Q-Fano Threefolds of Large Fano Index, I”, Doc. Math., 15 (2010), 843–872  mathscinet  zmath  isi
    25. Jihong Su, Yicai Zhao, “Relations of Normal Bundles and Flips of Small Contractions on Projective Manifolds”, Algebra Colloq, 17:01 (2010), 11  crossref
    26. Vyacheslav V. Shokurov, Sung Rak Choi, “Geography of log models: theory and applications”, centr.eur.j.math, 2011  crossref
    27. Yoshiaki Fukuma, “Effective non-vanishing of global sections of multiple adjoint bundles for polarized 3-folds”, Journal of Pure and Applied Algebra, 215:2 (2011), 168  crossref
    28. Yoshiaki Fukuma, “Effective non-vanishing of global sections of multiple adjoint bundles for polarized 4-folds”, Journal of Pure and Applied Algebra, 2012  crossref
    29. Yu. G. Prokhorov, “Fano threefolds of large Fano index and large degree”, Sb. Math., 204:3 (2013), 347–382  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
    30. Yoshiaki Fukuma, “On classification of polarized 3-folds
      $$(X,L)$$
      ( X , L ) with
      $$h^{0}(K_{X}+2L)=2$$
      h 0 ( K X + 2 L ) = 2”, Beitr Algebra Geom, 2013  crossref
    31. YOSHIAKI FUKUMA, “EFFECTIVE NON-VANISHING OF GLOBAL SECTIONS OF MULTIPLE ADJOINT BUNDLES FOR QUASI-POLARIZED n-FOLDS”, J. Algebra Appl, 2014, 1450046  crossref
    32. Yuri G. Prokhorov, “$\mathbb Q$-Fano threefolds of index $7$”, Proc. Steklov Inst. Math., 294 (2016), 139–153  mathnet  crossref  crossref  mathscinet  isi  elib  elib
    33. Birkar C., “Existence of flips and minimal models for 3-folds in char $p$”, Ann. Sci. Ec. Norm. Super., 49:1 (2016), 169–212  crossref  mathscinet  zmath  isi
    34. Yu. G. Prokhorov, “The rationality problem for conic bundles”, Russian Math. Surveys, 73:3 (2018), 375–456  mathnet  crossref  crossref  adsnasa  isi  elib
    35. Cheltsov I. Przyjalkowski V. Shramov C., “Which Quartic Double Solids Are Rational?”, J. Algebr. Geom., 28:2 (2019), 201–243  crossref  mathscinet  zmath  isi  scopus
  • Известия Академии наук СССР. Серия математическая Izvestiya: Mathematics
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