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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.
DOI:
https://doi.org/10.4213/im637
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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
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http://mi.mathnet.ru/eng/izv637https://doi.org/10.4213/im637 http://mi.mathnet.ru/eng/izv/v69/i2/p145
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Jahnke P., Peternell Th., Radloff I., “Threefolds with big and nef anticanonical bundles. I”, Math. Ann., 333:3 (2005), 569–631
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Yu. G. Prokhorov, “On Fano–Enriques threefolds”, Sb. Math., 198:4 (2007), 559–574
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Cheltsov I., “Nonrational del Pezzo fibrations”, Adv. Geom., 8:3 (2008), 441–450
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I. V. Karzhemanov, “On Fano threefolds with canonical Gorenstein singularities”, Sb. Math., 200:8 (2009), 1215–1246
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Priska Jahnke, Thomas Peternell, Ivo Radloff, “Threefolds with big and nef anticanonical bundles II”, centr.eur.j.math, 2011
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Cynk S., Rams S., “Defect via differential forms with logarithmic poles”, Math Nachr, 284:17–18 (2011), 2148–2158
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Karzhemanov I., “On some Fano-Enriques threefolds”, Adv Geom, 11:1 (2011), 117–129
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Prokhorov Yu., “Simple Finite Subgroups of the Cremona Group of Rank 3”, J. Algebr. Geom., 21:3 (2012), 563–600
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Yu. G. Prokhorov, “On birational involutions of $\mathbb P^3$”, Izv. Math., 77:3 (2013), 627–648
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Yu. G. Prokhorov, “On $G$-Fano threefolds”, Izv. Math., 79:4 (2015), 795–808
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V. V. Przyjalkowski, “Calabi-Yau compactifications of toric Landau-Ginzburg models for smooth Fano threefolds”, Sb. Math., 208:7 (2017), 992–1013
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Yuri Prokhorov, Constantin Shramov, “Jordan constant for Cremona group of rank $3$”, Mosc. Math. J., 17:3 (2017), 457–509
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Debarre O. Kuznetsov A., “Gushel-Mukai Varieties: Classification and Birationalities”, Algebraic Geom., 5:1 (2018), 15–76
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Prokhorov Yu. Shramov C., “P-Subgroups in the Space Cremona Group”, Math. Nachr., 291:8-9 (2018), 1374–1389
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Yu. G. Prokhorov, “The rationality problem for conic bundles”, Russian Math. Surveys, 73:3 (2018), 375–456
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V. V. Przyjalkowski, “Toric Landau–Ginzburg models”, Russian Math. Surveys, 73:6 (2018), 1033–1118
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V. V. Przyjalkowski, I. A. Cheltsov, K. A. Shramov, “Fano threefolds with infinite automorphism groups”, Izv. Math., 83:4 (2019), 860–907
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Yuri G. Prokhorov, “Rationality of Fano Threefolds with Terminal Gorenstein Singularities. I”, Proc. Steklov Inst. Math., 307 (2019), 210–231
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