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Izvestiya: Mathematics, 2004, Volume 68, Issue 2, Pages 429–434
DOI: https://doi.org/10.1070/IM2004v068n02ABEH000481 (Mi im481) 		 
This article is cited in 7 scientific papers (total in 7 papers)

Conic bundles with big discriminant loci

I. A. Cheltsov
English version PDF (141 kB) Citations (7) Russian version article
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DOI: https://doi.org/10.1070/IM2004v068n02ABEH000481
Abstract: We prove that conic bundles with sufficiently big discriminant locus cannot be birationally transformed into fibrations whose generic fibre has numerically trivial canonical divisor.
Received: 01.09.2003
Bibliographic databases:
UDC: 513.6
MSC: 14M22, 14E05
Language: English
Original paper language: Russian
Citation: I. A. Cheltsov, “Conic bundles with big discriminant loci”, Izv. Math., 68:2 (2004), 429–434
Citation in format AMSBIB
\Bibitem{Che04}
\by I.~A.~Cheltsov
\paper Conic bundles with big discriminant loci
\jour Izv. Math.
\yr 2004
\vol 68
\issue 2
\pages 429--434
\mathnet{http://mi.mathnet.ru/eng/im481}
\crossref{https://doi.org/10.1070/IM2004v068n02ABEH000481}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=2058006}
\zmath{https://zbmath.org/?q=an:1078.14014}
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\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-33746524354}
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  • https://www.mathnet.ru/eng/im/v68/i2/p215
    • This publication is cited in the following 7 articles:
    1. Yu. G. Prokhorov, “The rationality problem for conic bundles”, Russian Math. Surveys, 73:3 (2018), 375–456  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
    2. Kollar J., “Conic Bundles That Are Not Birational to Numerical Calabi-Yau Pairs”, Epijournal Geom. Algebr., 1 (2017), UNSP 1  mathscinet  isi
    3. A. V. Pukhlikov, “Birational geometry of higher-dimensional Fano varieties”, Proc. Steklov Inst. Math., 288, suppl. 2 (2015), S1–S150  mathnet  crossref  crossref  isi  elib
    4. Ivan Cheltsov, Jihun Park, Progress in Mathematics, 282, Cohomological and Geometric Approaches to Rationality Problems, 2010, 75  crossref
    5. A. V. Pukhlikov, “Birationally rigid varieties. I. Fano varieties”, Russian Math. Surveys, 62:5 (2007), 857–942  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  elib
    6. Pukhlikov A.V., “Birational geometry of algebraic varieties with a pencil of Fano complete intersections”, Manuscripta Math., 121:4 (2006), 491–526  crossref  mathscinet  zmath  isi  elib  scopus
    7. I. A. Cheltsov, “Birationally superrigid cyclic triple spaces”, Izv. Math., 68:6 (2004), 1229–1275  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    		Известия Российской академии наук. Серия математическая Izvestiya: Mathematics
    Statistics & downloads:
    Abstract page:550
    Russian version PDF:232
    English version PDF:17
    References:78
    First page:1
     
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