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Izvestiya: Mathematics, 2005, Volume 69, Issue 2, Pages 365–421
DOI: https://doi.org/10.1070/IM2005v069n02ABEH000533
(Mi im637)
 

This article is cited in 33 scientific papers (total in 33 papers)

Hyperelliptic and trigonal Fano threefolds

V. V. Przyjalkowski, I. A. Cheltsov, K. A. Shramov

Steklov Mathematical Institute, Russian Academy of Sciences
References:
Abstract: We classify Fano 3-folds with canonical Gorenstein singularities whose anticanonical linear system has no base points but does not give an embedding, and we classify anticanonically embedded Fano 3-folds with canonical Gorenstein singularities which are not intersections of quadrics. We also study rationality questions for most of these varieties.
Received: 01.07.2004
Bibliographic databases:
Document Type: Article
UDC: 512.76
Language: English
Original paper language: Russian
Citation: V. V. Przyjalkowski, I. A. Cheltsov, K. A. Shramov, “Hyperelliptic and trigonal Fano threefolds”, Izv. Math., 69:2 (2005), 365–421
Citation in format AMSBIB
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\by V.~V.~Przyjalkowski, I.~A.~Cheltsov, K.~A.~Shramov
\paper Hyperelliptic and trigonal Fano threefolds
\jour Izv. Math.
\yr 2005
\vol 69
\issue 2
\pages 365--421
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Linking options:
  • https://www.mathnet.ru/eng/im637
  • https://doi.org/10.1070/IM2005v069n02ABEH000533
  • https://www.mathnet.ru/eng/im/v69/i2/p145
  • This publication is cited in the following 33 articles:
    1. Ciro Ciliberto, “On the rationality of certain Fano threefolds”, manuscripta math., 174:1-2 (2024), 203  crossref
    2. Alexander Kuznetsov, Evgeny Shinder, “Derived categories of Fano threefolds and degenerations”, Invent. math., 2024  crossref
    3. Jérémy Blanc, Ivan Cheltsov, Alexander Duncan, Yuri Prokhorov, “Finite quasisimple groups acting on rationally connected threefolds”, Math. Proc. Camb. Philos. Soc., 174:3 (2023), 531–568  mathnet  crossref
    4. Yuri Prokhorov, “Rationality of Fano threefolds with terminal Gorenstein singularities, II”, Rend. Circ. Mat. Palermo (2), 72 (2023), 1797–1821  mathnet  crossref  scopus
    5. Nguyen Thi Anh Hang Hoff M. Hoang Le Truong, “On Cylindrical Smooth Rational Fano Fourfolds”, J. Korean. Math. Soc., 59:1 (2022), 87–103  crossref  mathscinet  isi  scopus
    6. Yu. G. Prokhorov, “Trekhmernye mnogoobraziya Fano”, Lekts. kursy NOTs, 31, MIAN, M., 2022, 3–154  mathnet  crossref
    7. Ciliberto C. Zaidenberg M., “Lines, Conics, and All That”, Pure Appl. Math. Q., 18:1 (2022), 101–176  crossref  mathscinet  isi
    8. Karzhemanov I., “Rationality of An S-6-Invariant Quartic 3-Fold”, Bull. Braz. Math. Soc., 51:1 (2020), 169–184  crossref  mathscinet  isi
    9. 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  zmath  adsnasa  isi  elib
    10. Yuri G. Prokhorov, “Rationality of Fano Threefolds with Terminal Gorenstein Singularities. I”, Proc. Steklov Inst. Math., 307 (2019), 210–231  mathnet  crossref  crossref  isi  elib
    11. Liu J., “Second Chern Class of Fano Manifolds and Anti-Canonical Geometry”, Math. Ann., 375:1-2 (2019), 655–669  crossref  mathscinet  isi
    12. Sławomir Cynk, “Defect formula for nodal complete intersection threefolds”, Int. J. Math., 30:04 (2019), 1950020  crossref
    13. Debarre O. Kuznetsov A., “Gushel-Mukai Varieties: Classification and Birationalities”, Algebraic Geom., 5:1 (2018), 15–76  crossref  mathscinet  isi  scopus
    14. Prokhorov Yu. Shramov C., “P-Subgroups in the Space Cremona Group”, Math. Nachr., 291:8-9 (2018), 1374–1389  crossref  mathscinet  zmath  isi  scopus
    15. 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
    16. V. V. Przyjalkowski, “Toric Landau–Ginzburg models”, Russian Math. Surveys, 73:6 (2018), 1033–1118  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
    17. 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
    18. Yuri Prokhorov, Constantin Shramov, “Jordan constant for Cremona group of rank 3”, Mosc. Math. J., 17:3 (2017), 457–509  mathnet  crossref  mathscinet
    19. Jan Arthur Christophersen, Nathan Ilten, “Hilbert schemes and toric degenerations for low degree Fano threefolds”, Journal für die reine und angewandte Mathematik (Crelles Journal), 2016:717 (2016), 77  crossref
    20. Yu. G. Prokhorov, “On G-Fano threefolds”, Izv. Math., 79:4 (2015), 795–808  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  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
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    References:115
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