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Izv. RAN. Ser. Mat., 1992, Volume 56, Issue 1, Pages 105–203 (Mi izv960)  

This article is cited in 103 scientific papers (total in 104 papers)

Three-fold log flips

V. V. Shokurov


Abstract: We prove that 3-fold log flips exist. We deduce the existence of log canonical and $\mathbf Q$-factorial log terminal models, as well as a positive answer to the inversion problem for log canonical and log terminal adjunction.

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English version:
Russian Academy of Sciences. Izvestiya Mathematics, 1993, 40:1, 95–202

Bibliographic databases:

UDC: 512.7
MSC: 14E05, 14E35, 14J30

Citation: V. V. Shokurov, “Three-fold log flips”, Izv. RAN. Ser. Mat., 56:1 (1992), 105–203; Russian Acad. Sci. Izv. Math., 40:1 (1993), 95–202

Citation in format AMSBIB
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\by V.~V.~Shokurov
\paper Three-fold log flips
\jour Izv. RAN. Ser. Mat.
\yr 1992
\vol 56
\issue 1
\pages 105--203
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\zmath{https://zbmath.org/?q=an:0785.14023}
\adsnasa{http://adsabs.harvard.edu/cgi-bin/bib_query?1993IzMat..40...95S}
\transl
\jour Russian Acad. Sci. Izv. Math.
\yr 1993
\vol 40
\issue 1
\pages 95--202
\crossref{https://doi.org/10.1070/IM1993v040n01ABEH001862}
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    Addendum

    This publication is cited in the following articles:
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    36. 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
    37. Yu. G. Prokhorov, “On the degree of Fano threefolds with canonical Gorenstein singularities”, Sb. Math., 196:1 (2005), 77–114  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
    38. 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
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    40. A. V. Pukhlikov, “Birational geometry of Fano direct products”, Izv. Math., 69:6 (2005), 1225–1255  mathnet  crossref  crossref  mathscinet  zmath  isi  elib  elib
    41. D. A. Stepanov, “On nonrational divisors over non-Gorenstein terminal singularities”, J. Math. Sci., 142:2 (2007), 1977–1988  mathnet  crossref  mathscinet  zmath  elib  elib
    42. I. A. Cheltsov, “Local inequalities and birational superrigidity of Fano varieties”, Izv. Math., 70:3 (2006), 605–639  mathnet  crossref  crossref  mathscinet  zmath  isi  elib  elib
    43. I. A. Cheltsov, “Factoriality of nodal three-dimensional varieties and connectedness of the locus of log canonical singularities”, Sb. Math., 197:3 (2006), 387–414  mathnet  crossref  crossref  mathscinet  zmath  isi  elib  elib
    44. “ON THE PROJECTIVE FOURFOLDS WITH ALMOST NUMERICALLY POSITIVE CANONICAL DIVISORS”, Bulletin of the Korean Mathematical Society, 43:4 (2006), 763  crossref
    45. Yu. G. Prokhorov, “The degree of $\mathbb Q$-Fano threefolds”, Sb. Math., 198:11 (2007), 1683–1702  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
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    47. I. A. Cheltsov, “Elliptic structures on weighted three-dimensional Fano hypersurfaces”, Izv. Math., 71:4 (2007), 765–862  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
    48. A. V. Pukhlikov, “Explicit examples of birationally rigid Fano varieties”, Mosc. Math. J., 7:3 (2007), 543–560  mathnet  crossref  mathscinet  zmath
    49. I. A. Cheltsov, K. A. Shramov, “Log canonical thresholds of smooth Fano threefolds”, Russian Math. Surveys, 63:5 (2008), 859–958  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  elib
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    54. 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
    55. I. A. Cheltsov, K. A. Shramov, “Extremal Metrics on del Pezzo Threefolds”, Proc. Steklov Inst. Math., 264 (2009), 30–44  mathnet  crossref  mathscinet  isi  elib  elib
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    59. Druel S., “Existence of Minimal Models for General Type Varieties”, Asterisque, 2009, no. 326, 1–38  mathscinet  zmath  isi
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    61. R. J. Mullany, “Fano Double Spaces with a Big Singular Locus”, Math. Notes, 87:3 (2010), 444–448  mathnet  crossref  crossref  mathscinet  zmath  isi
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    64. C. Birkar, V. V. Shokurov, “Mld's vs thresholds and flips”, Journal für die reine und angewandte Mathematik (Crelles Journal), 2010:638 (2010), 209  crossref  elib
    65. Fujino O., “Theory of Non-Lc Ideal Sheaves: Basic Properties”, Kyoto J. Math., 50:2 (2010), 225–245  crossref  mathscinet  zmath  isi
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    70. Shokurov V.V., Choi S.R., “Geography of log models: theory and applications”, Cent Eur J Math, 9:3 (2011), 489–534  crossref  isi
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  • Известия Российской академии наук. Серия математическая Izvestiya: Mathematics
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