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Izv. RAN. Ser. Mat., 2005, Volume 69, Issue 2, Pages 145–204 (Mi izv637)  

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

Hyperelliptic and trigonal Fano threefolds

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

Steklov Mathematical Institute, Russian Academy of Sciences

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.


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English version:
Izvestiya: Mathematics, 2005, 69:2, 365–421

Bibliographic databases:

UDC: 512.76
MSC: 14J45, 14J30, 14J17, 14E08, 14E05
Received: 01.07.2004

Citation: V. V. Przyjalkowski, I. A. Cheltsov, K. A. Shramov, “Hyperelliptic and trigonal Fano threefolds”, Izv. RAN. Ser. Mat., 69:2 (2005), 145–204; Izv. Math., 69:2 (2005), 365–421

Citation in format AMSBIB
\by V.~V.~Przyjalkowski, I.~A.~Cheltsov, K.~A.~Shramov
\paper Hyperelliptic and trigonal Fano threefolds
\jour Izv. RAN. Ser. Mat.
\yr 2005
\vol 69
\issue 2
\pages 145--204
\jour Izv. Math.
\yr 2005
\vol 69
\issue 2
\pages 365--421

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    This publication is cited in the following articles:
    1. Jahnke P., Peternell Th., Radloff I., “Threefolds with big and nef anticanonical bundles. I”, Math. Ann., 333:3 (2005), 569–631  crossref  mathscinet  zmath  isi  scopus
    2. K. A. Shramov, “On the rationality of non-singular threefolds with a pencil of Del Pezzo surfaces of degree 4”, Sb. Math., 197:1 (2006), 127–137  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
    3. Yu. G. Prokhorov, “On Fano–Enriques threefolds”, Sb. Math., 198:4 (2007), 559–574  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
    4. Cheltsov I., “Nonrational del Pezzo fibrations”, Adv. Geom., 8:3 (2008), 441–450  crossref  mathscinet  zmath  isi  scopus
    5. I. V. Karzhemanov, “On Fano threefolds with canonical Gorenstein singularities”, Sb. Math., 200:8 (2009), 1215–1246  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
    6. Priska Jahnke, Thomas Peternell, Ivo Radloff, “Threefolds with big and nef anticanonical bundles II”, centr.eur.j.math, 2011  crossref  mathscinet  isi  scopus
    7. Cynk S., Rams S., “Defect via differential forms with logarithmic poles”, Math Nachr, 284:17–18 (2011), 2148–2158  crossref  mathscinet  zmath  isi  elib  scopus
    8. Karzhemanov I., “On some Fano-Enriques threefolds”, Adv Geom, 11:1 (2011), 117–129  crossref  mathscinet  zmath  isi  scopus
    9. Prokhorov Yu., “Simple Finite Subgroups of the Cremona Group of Rank 3”, J. Algebr. Geom., 21:3 (2012), 563–600  crossref  mathscinet  zmath  isi  elib  scopus
    10. Yu. G. Prokhorov, “On birational involutions of $\mathbb P^3$”, Izv. Math., 77:3 (2013), 627–648  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  elib
    11. Yu. G. Prokhorov, “On $G$-Fano threefolds”, Izv. Math., 79:4 (2015), 795–808  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  elib
    12. 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
    13. Yuri Prokhorov, Constantin Shramov, “Jordan constant for Cremona group of rank $3$”, Mosc. Math. J., 17:3 (2017), 457–509  mathnet  crossref  mathscinet
    14. Debarre O. Kuznetsov A., “Gushel-Mukai Varieties: Classification and Birationalities”, Algebraic Geom., 5:1 (2018), 15–76  crossref  mathscinet  isi  scopus
    15. Prokhorov Yu. Shramov C., “P-Subgroups in the Space Cremona Group”, Math. Nachr., 291:8-9 (2018), 1374–1389  crossref  mathscinet  zmath  isi  scopus
    16. Yu. G. Prokhorov, “The rationality problem for conic bundles”, Russian Math. Surveys, 73:3 (2018), 375–456  mathnet  crossref  crossref  mathscinet  adsnasa  isi  elib
    17. V. V. Przyjalkowski, “Toric Landau–Ginzburg models”, Russian Math. Surveys, 73:6 (2018), 1033–1118  mathnet  crossref  crossref  mathscinet  adsnasa  isi  elib
    18. 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
    19. 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
  • Известия Российской академии наук. Серия математическая Izvestiya: Mathematics
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