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Izv. Akad. Nauk SSSR Ser. Mat., 1979, Volume 43, Issue 4, Pages 922–964 (Mi izv1741)  

This article is cited in 19 scientific papers (total in 20 papers)

The existence of a straight line on Fano 3-folds

V. V. Shokurov

Abstract: In this paper is shown the existence of a straight line on a Fano 3-fold of the principal series (under the anticanonical embedding) if the 3-fold has index 1 and is not isomorphic to the product $\mathbf P^1\times\mathbf P^2$.
Bibliography: 13 titles.

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English version:
Mathematics of the USSR-Izvestiya, 1980, 15:1, 173–209

Bibliographic databases:

UDC: 513.6
MSC: Primary 14M20, 14J99; Secondary 14E35, 14N05
Received: 13.07.1978

Citation: V. V. Shokurov, “The existence of a straight line on Fano 3-folds”, Izv. Akad. Nauk SSSR Ser. Mat., 43:4 (1979), 922–964; Math. USSR-Izv., 15:1 (1980), 173–209

Citation in format AMSBIB
\by V.~V.~Shokurov
\paper The existence of a~straight line on Fano 3-folds
\jour Izv. Akad. Nauk SSSR Ser. Mat.
\yr 1979
\vol 43
\issue 4
\pages 922--964
\jour Math. USSR-Izv.
\yr 1980
\vol 15
\issue 1
\pages 173--209

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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. I. V. Demin, “Fano threefolds representable in the form of line bundles”, Math. USSR-Izv., 17:1 (1981), 219–226  mathnet  crossref  mathscinet  zmath  isi
    2. S. M. L'vovskii, “Boundedness of the degree of Fano threefolds”, Math. USSR-Izv., 19:3 (1982), 521–558  mathnet  crossref  mathscinet  zmath
    3. D. G. Markushevich, “Numerical invariants of families of lines on some Fano varieties”, Math. USSR-Sb., 44:2 (1983), 239–260  mathnet  crossref  mathscinet  zmath
    4. N. P. Gushel', “On Fano varieties of genus 6”, Math. USSR-Izv., 21:3 (1983), 445–459  mathnet  crossref  mathscinet  zmath
    5. N. P. Gushel', “Fano varieties of genus 8”, Russian Math. Surveys, 38:1 (1983), 192–193  mathnet  crossref  mathscinet  zmath  adsnasa  isi
    6. Yu. I. Manin, M. A. Tsfasman, “Rational varieties: algebra, geometry and arithmetic”, Russian Math. Surveys, 41:2 (1986), 51–116  mathnet  crossref  mathscinet  zmath  adsnasa  isi
    7. V. A. Iskovskikh, “Double projection from a line on Fano threefolds of the first kind”, Math. USSR-Sb., 66:1 (1990), 265–284  mathnet  crossref  mathscinet  zmath  isi
    8. Y. Ruan, “Symplectic topology and extremal rays”, GAFA Geom funct anal, 3:4 (1993), 395  crossref  mathscinet  zmath
    9. I. A. Cheltsov, “Rationality of an Enriques–Fano threefold of genus five”, Izv. Math., 68:3 (2004), 607–618  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
    10. I. A. Cheltsov, “Birationally rigid Fano varieties”, Russian Math. Surveys, 60:5 (2005), 875–965  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  elib
    11. V. V. Przyjalkowski, I. A. Cheltsov, K. A. Shramov, “Hyperelliptic and trigonal Fano threefolds”, Izv. Math., 69:2 (2005), 365–421  mathnet  crossref  crossref  mathscinet  zmath  isi  elib  elib
    12. Antonio Lanteri, Hidetoshi Maeda, “Ample vector bundles with zero loci having a bielliptic curve section of low degree”, Geom Dedicata, 131:1 (2008), 111  crossref  mathscinet  zmath  isi
    13. 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
    14. F. A. Bogomolov, Vik. S. Kulikov, Yu. I. Manin, V. V. Nikulin, D. O. Orlov, A. N. Parshin, Yu. G. Prokhorov, A. V. Pukhlikov, M. Reid, I. R. Shafarevich, V. V. Shokurov, “Vasilii Alekseevich Iskovskikh (obituary)”, Russian Math. Surveys, 64:5 (2009), 939–946  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
    15. F. FLAMINI, E. SERNESI, “THE CURVE OF LINES ON A PRIME FANO THREE-FOLD OF GENUS 8”, Int. J. Math, 21:12 (2010), 1561  crossref
    16. Kento Fujita, “Around the Mukai conjecture for Fano manifolds”, European Journal of Mathematics, 2015  crossref
    17. Yu. G. Prokhorov, “On $G$-Fano threefolds”, Izv. Math., 79:4 (2015), 795–808  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  elib
    18. Prokhorov Yu. Zaidenberg M., “New Examples of Cylindrical Fano Fourfolds”, Algebraic Varieties and Automorphism Groups, Advanced Studies in Pure Mathematics, 75, ed. Masuda K. Kishimoto T. Kojima H. Miyanishi M. Zaidenberg M., Math Soc Japan, 2017, 443–463  isi
    19. Kuznetsov A.G. Prokhorov Yu.G. Shramov C.A., “Hilbert Schemes of Lines and Conics and Automorphism Groups of Fano Threefolds”, Jap. J. Math., 13:1 (2018), 109–185  crossref  isi
    20. Prokhorov Yu. Zaidenberg M., “Fano-Mukai Fourfolds of Genus 10 as Compactifications of C-4”, Eur. J. Math., 4:3, 2, SI (2018), 1197–1263  crossref  mathscinet  isi  scopus
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