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.
This publication is cited in the following 33 articles:
Ciro Ciliberto, “On the rationality of certain Fano threefolds”, manuscripta math., 174:1-2 (2024), 203
Alexander Kuznetsov, Evgeny Shinder, “Derived categories of Fano threefolds and degenerations”, Invent. math., 2024
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
Yuri Prokhorov, “Rationality of Fano threefolds with terminal Gorenstein singularities, II”, Rend. Circ. Mat. Palermo (2), 72 (2023), 1797–1821
Nguyen Thi Anh Hang Hoff M. Hoang Le Truong, “On Cylindrical Smooth Rational Fano Fourfolds”, J. Korean. Math. Soc., 59:1 (2022), 87–103
Yu. G. Prokhorov, “Trekhmernye mnogoobraziya Fano”, Lekts. kursy NOTs, 31, MIAN, M., 2022, 3–154
Ciliberto C. Zaidenberg M., “Lines, Conics, and All That”, Pure Appl. Math. Q., 18:1 (2022), 101–176
Karzhemanov I., “Rationality of An S-6-Invariant Quartic 3-Fold”, Bull. Braz. Math. Soc., 51:1 (2020), 169–184
V. V. Przyjalkowski, I. A. Cheltsov, K. A. Shramov, “Fano threefolds with infinite automorphism groups”, Izv. Math., 83:4 (2019), 860–907
Yuri G. Prokhorov, “Rationality of Fano Threefolds with Terminal Gorenstein Singularities. I”, Proc. Steklov Inst. Math., 307 (2019), 210–231
Liu J., “Second Chern Class of Fano Manifolds and Anti-Canonical Geometry”, Math. Ann., 375:1-2 (2019), 655–669
Sławomir Cynk, “Defect formula for nodal complete intersection threefolds”, Int. J. Math., 30:04 (2019), 1950020
Debarre O. Kuznetsov A., “Gushel-Mukai Varieties: Classification and Birationalities”, Algebraic Geom., 5:1 (2018), 15–76
Prokhorov Yu. Shramov C., “P-Subgroups in the Space Cremona Group”, Math. Nachr., 291:8-9 (2018), 1374–1389
Yu. G. Prokhorov, “The rationality problem for conic bundles”, Russian Math. Surveys, 73:3 (2018), 375–456
V. V. Przyjalkowski, “Toric Landau–Ginzburg models”, Russian Math. Surveys, 73:6 (2018), 1033–1118
V. V. Przyjalkowski, “Calabi-Yau compactifications of toric Landau-Ginzburg models for smooth Fano threefolds”, Sb. Math., 208:7 (2017), 992–1013
Yuri Prokhorov, Constantin Shramov, “Jordan constant for Cremona group of rank 3”, Mosc. Math. J., 17:3 (2017), 457–509
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