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Mat. Sb., 1997, Volume 188, Number 11, Pages 99–120 (Mi msb277)  

This article is cited in 6 scientific papers (total in 6 papers)

On the existence of complements of the canonical divisor for Mori conic bundles

Yu. G. Prokhorov

M. V. Lomonosov Moscow State University

Abstract: This paper continues the author's study of extremal contractions in the sense of Mori from three-dimensional varieties onto surfaces. Such contractions occur in a natural way in the birational classification theory of three-dimensional algebraic varieties. Reid's “general elephant” conjecture of the complementedness of the canonical divisor and also the conjecture about singularities of the base surface are discussed. The situation is studied locally near a singular fibre.

DOI: https://doi.org/10.4213/sm277

Full text: PDF file (366 kB)
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English version:
Sbornik: Mathematics, 1997, 188:11, 1665–1685

Bibliographic databases:

UDC: 512.7
MSC: 14J30, 14E35
Received: 21.01.1997

Citation: Yu. G. Prokhorov, “On the existence of complements of the canonical divisor for Mori conic bundles”, Mat. Sb., 188:11 (1997), 99–120; Sb. Math., 188:11 (1997), 1665–1685

Citation in format AMSBIB
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\paper On the existence of complements of the~canonical divisor for Mori conic bundles
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\pages 99--120
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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. S. A. Kudryavtsev, “Classification of three-dimensional exceptional log canonical hypersurface singularities. I”, Izv. Math., 66:5 (2002), 949–1034  mathnet  crossref  crossref  mathscinet  zmath  elib
    2. Takagi, H, “On classification of Q-Fano 3-folds of Gorenstein index 2. I”, Nagoya Mathematical Journal, 167 (2002), 117  crossref  mathscinet  zmath  isi  scopus  scopus
    3. Mori, S, “On Q-conic bundles, II”, Publications of the Research Institute For Mathematical Sciences, 44:3 (2008), 955  crossref  mathscinet  zmath  isi  scopus  scopus
    4. Mori, S, “On Q-conic bundles”, Publications of the Research Institute For Mathematical Sciences, 44:2 (2008), 315  crossref  mathscinet  zmath  isi  scopus  scopus  scopus
    5. Mori Sh., Prokhorov Yu., “Threefold extremal contractions of type (IA)”, Kyoto Journal of Mathematics, 51:2 (2011), 393–438  crossref  mathscinet  zmath  isi  scopus  scopus
    6. Yu. G. Prokhorov, “The rationality problem for conic bundles”, Russian Math. Surveys, 73:3 (2018), 375–456  mathnet  crossref  crossref  adsnasa  isi  elib
  • Математический сборник - 1992–2005 Sbornik: Mathematics (from 1967)
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