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Izv. Akad. Nauk SSSR Ser. Mat., 1977, Volume 41, Issue 3, Pages 516–562 (Mi izv1823)  

This article is cited in 59 scientific papers (total in 60 papers)

Fano 3-folds. I

V. A. Iskovskikh


Abstract: This article contains a classification of special Fano varieties; we give a description of the projective models of Fano 3-folds of index $r\geqslant2$ and of hyperelliptic Fano 3-folds.
Bibliography: 31 titles.

Full text: PDF file (4953 kB)
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English version:
Mathematics of the USSR-Izvestiya, 1977, 11:3, 485–527

Bibliographic databases:

UDC: 513.6
MSC: Primary 14J10; Secondary 14N05, 14M20
Received: 07.08.1975
Revised: 23.12.1976

Citation: V. A. Iskovskikh, “Fano 3-folds. I”, Izv. Akad. Nauk SSSR Ser. Mat., 41:3 (1977), 516–562; Math. USSR-Izv., 11:3 (1977), 485–527

Citation in format AMSBIB
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\by V.~A.~Iskovskikh
\paper Fano 3-folds.~I
\jour Izv. Akad. Nauk SSSR Ser. Mat.
\yr 1977
\vol 41
\issue 3
\pages 516--562
\mathnet{http://mi.mathnet.ru/izv1823}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=463151}
\zmath{https://zbmath.org/?q=an:0363.14010|0382.14013}
\transl
\jour Math. USSR-Izv.
\yr 1977
\vol 11
\issue 3
\pages 485--527
\crossref{https://doi.org/10.1070/IM1977v011n03ABEH001733}


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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles
    Cycle of papers
    • Fano 3-folds. I
      V. A. Iskovskikh
      Izv. Akad. Nauk SSSR Ser. Mat., 1977, 41:3, 516–562
    • Fano 3-folds. II
      V. A. Iskovskikh
      Izv. Akad. Nauk SSSR Ser. Mat., 1978, 42:3, 506–549


    This publication is cited in the following articles:
    1. V. A. Iskovskikh, “Fano 3-folds. II”, Math. USSR-Izv., 12:3 (1978), 469–506  mathnet  crossref  mathscinet  zmath
    2. V. A. Iskovskikh, “On Fano varieties of the first kind”, Russian Math. Surveys, 33:3 (1978), 155–156  mathnet  crossref  mathscinet  zmath
    3. V. V. Shokurov, “Smoothness of the general anticanonical divisor on a Fano 3-fold”, Math. USSR-Izv., 14:2 (1980), 395–405  mathnet  crossref  mathscinet  zmath  isi
    4. V. V. Shokurov, “The existence of a straight line on Fano 3-folds”, Math. USSR-Izv., 15:1 (1980), 173–209  mathnet  crossref  mathscinet  zmath  adsnasa  isi
    5. A. S. Tikhomirov, “The geometry of the Fano surface of the double cover of $P^3$ branched in a quartic”, Math. USSR-Izv., 16:2 (1981), 373–397  mathnet  crossref  mathscinet  zmath  isi
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    7. A. S. Tikhomirov, “The Fano surface of the Veronese double cone”, Math. USSR-Izv., 19:2 (1982), 377–443  mathnet  crossref  mathscinet  zmath
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    11. 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
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    15. Atanas Iliev, “Lines on the Gushel' threefold”, Indagationes Mathematicae, 5:3 (1994), 307  crossref
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    17. Antonio Lanteri, Gianluca Occhetta, “Double Covers of Some Fano Manifolds as Hyperplane Sections”, Math Nachr, 193:1 (1998), 93  crossref
    18. A. I. Kostrikin, V. S. Kulikov, Yu. I. Manin, V. V. Nikulin, A. N. Parshin, Yu. G. Prokhorov, A. V. Pukhlikov, M. Reid, A. N. Tyurin, I. R. Shafarevich, V. V. Shokurov, “Vasilii Alekseevich Iskovskikh (on his 60th birthday)”, Russian Math. Surveys, 54:4 (1999), 863–868  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi
    19. V. V. Batyrev, “On the classification of toric Fano 4-folds”, J Math Sci, 94:1 (1999), 1021  crossref
    20. Enrique Arrondo, Laura Costa, “Vector bundles on fano 3-folds without intermediate cohomology”, Communications in Algebra, 28:8 (2000), 3899  crossref
    21. Thomas peternell, Andrew J. Sommese, “Ample vector bundles and branched coverings”, Communications in Algebra, 28:12 (2000), 5573  crossref
    22. 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
    23. A. G. Kuznetsov, “Derived Categories of Cubic and $V_{14}$”, Proc. Steklov Inst. Math., 246 (2004), 171–194  mathnet  mathscinet  zmath
    24. Seunghun Lee, “Linear Systems on Fano Threefolds. I”, Communications in Algebra, 32:7 (2004), 2711  crossref
    25. Priska Jahnke, Thomas Peternell, Ivo Radloff, “Threefolds with big and nef anticanonical bundles I”, Math Ann, 333:3 (2005), 569  crossref  mathscinet  zmath  isi
    26. I. A. Cheltsov, “Birationally rigid Fano varieties”, Russian Math. Surveys, 60:5 (2005), 875–965  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  elib
    27. 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
    28. A. G. Kuznetsov, “Derived Categories of Fano Threefolds $V_{12}$”, Math. Notes, 78:4 (2005), 537–550  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
    29. Priska Jahnke, Ivo Radloff, “Fano threefolds with sections in Ω1V (1)”, Math Nachr, 280:1-2 (2007), 127  crossref  mathscinet  zmath  isi
    30. V. V. Przyjalkowski, “Quantum cohomology of smooth complete intersections in weighted projective spaces and in singular toric varieties”, Sb. Math., 198:9 (2007), 1325–1340  mathnet  crossref  crossref  mathscinet  zmath  isi  elib  elib
    31. M. C. Beltrametti, C. Ciliberto, A. Lanteri, A. J. Sommese, “On the Birationality of the Bicanonical Map of a Surface Section of a Threefold”, Communications in Algebra, 35:5 (2007), 1627  crossref
    32. Takashi Kishimoto, “Affine threefolds whose log canonical bundles are not numerically effective”, Journal of Pure and Applied Algebra, 208:1 (2007), 189  crossref
    33. Thomas Peternell, Priska Jahnke, “Almost del Pezzo manifolds”, advg, 8:3 (2008), 387  crossref  mathscinet  zmath  isi
    34. 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
    35. Proc. Steklov Inst. Math., 264 (2009), 87–95  mathnet  crossref  mathscinet  isi  elib
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    37. Victor Batyrev, Dorothee Juny, “Classification of Gorenstein toric Del Pezzo varieties in arbitrary dimension”, Mosc. Math. J., 10:2 (2010), 285–316  mathnet  crossref  mathscinet
    38. Jaume Amorós, Indranil Biswas, “Compact Kähler manifolds with elliptic homotopy type”, Advances in Mathematics, 224:3 (2010), 1167  crossref
    39. John Davey, Amihay Hanany, Noppadol Mekareeya, Giuseppe Torri, “M2-branes and Fano 3-folds”, J. Phys. A: Math. Theor, 44:40 (2011), 405401  crossref
    40. David R. Morrison, Washington Taylor, “Matter and singularities”, J. High Energ. Phys, 2012:1 (2012)  crossref
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    42. Prokhorov Yu., “Simple Finite Subgroups of the Cremona Group of Rank 3”, J. Algebr. Geom., 21:3 (2012), 563–600  isi
    43. Ilten N.O., Lewis J., Przyjalkowski V., “Toric Degenerations of Fano Threefolds Giving Weak Landau-Ginzburg Models”, J. Algebra, 374 (2013), 104–121  crossref  isi
    44. V. V. Przyjalkowski, “Weak Landau–Ginzburg models for smooth Fano threefolds”, Izv. Math., 77:4 (2013), 772–794  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  elib
    45. M. S. Omelkova, “Semeistva gladkikh ratsionalnykh krivykh maloi stepeni na mnogoobraziyakh Fano stepeni 5 osnovnoi serii”, Model. i analiz inform. sistem, 20:3 (2013), 99–107  mathnet
    46. Faenzi D., “Even and Odd Instanton Bundles on Fano Threefolds of Picard Number One”, Manuscr. Math., 144:1-2 (2014), 199–239  crossref  isi
    47. Ilya Karzhemanov, “Fano threefolds with canonical Gorenstein singularities and big degree”, Math. Ann, 2014  crossref
    48. Fujita K., “Simple normal crossing Fano varieties and log Fano manifolds”, Nagoya Math. J., 214 (2014), 95–123  crossref  mathscinet  zmath  isi  scopus
    49. Kento Fujita, “Around the Mukai conjecture for Fano manifolds”, European Journal of Mathematics, 2015  crossref
    50. V. V. Golyshev, D. Zagier, “Proof of the gamma conjecture for Fano 3-folds of Picard rank 1”, Izv. Math., 80:1 (2016), 24–49  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
    51. Beauville A., “The Luroth Problem”, Rationality Problems in Algebraic Geometry, Lect. Notes Math., Lecture Notes in Mathematics, 2172, ed. Pardini R. Pirola G., Springer International Publishing Ag, 2016, 1–27  crossref  isi
    52. Sławomir Dinew, Grzegorz Kapustka, Michał Kapustka, “Remarks on Mukai threefolds admitting $\mathbb C^*$ action”, Mosc. Math. J., 17:1 (2017), 15–33  mathnet  crossref  mathscinet
    53. V. V. Przyjalkowski, “Calabi-Yau compactifications of toric Landau-Ginzburg models for smooth Fano threefolds”, Sb. Math., 208:7 (2017), 992–1013  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  elib
    54. Prokhorov Yu., Zaidenberg M., “New Examples of Cylindrical Fano Fourfolds”, Algebraic Varieties and Automorphism Groups, Advanced Studies in Pure Mathematics, 75, eds. Masuda K., Kishimoto T., Kojima H., Miyanishi M., Zaidenberg M., Math Soc Japan, 2017, 443–463  isi
    55. Debarre O. Kuznetsov A., “Gushel-Mukai Varieties: Classification and Birationalities”, Algebraic Geom., 5:1 (2018), 15–76  crossref  isi
    56. 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
    57. V. V. Przyjalkowski, “Toric Landau–Ginzburg models”, Russian Math. Surveys, 73:6 (2018), 1033–1118  mathnet  crossref  crossref  mathscinet  adsnasa  isi  elib
    58. V. V. Przyjalkowski, I. A. Cheltsov, K. A. Shramov, “Fano threefolds with infinite automorphism groups”, Izv. Math., 83:4 (2019), 860–907  mathnet  crossref  crossref  mathscinet  adsnasa  isi  elib
    59. Yuri G. Prokhorov, “Rationality of Fano Threefolds with Terminal Gorenstein Singularities. I”, Proc. Steklov Inst. Math., 307 (2019), 210–231  mathnet  crossref  crossref
    60. S. O. Gorchinskiy, Vik. S. Kulikov, A. N. Parshin, V. L. Popov, “Igor Rostislavovich Shafarevich and His Mathematical Heritage”, Proc. Steklov Inst. Math., 307 (2019), 1–21  mathnet  crossref  crossref
  • Известия Академии наук СССР. Серия математическая Izvestiya: Mathematics
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