Аннотация:
We classify Fano threefolds with only terminal singularities whose canonical class is Cartier and divisible by 2 with the additional assumption that the G-invariant part of the Weil divisor class group is of rank 1 with respect to an action of some group G. In particular, we find a lot of examples of Fano 3-folds with “many” symmetries.
The work was partially supported by RFBR grants Nos. 11-01-00336-a and 11-01-92613-KO_a, Leading Scientific Schools, No. 4713.2010.1, and AG Laboratory HSE, RF government grant ag. 11.G34.31.0023.
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Статья
Язык публикации: английский
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Эта публикация цитируется в следующих 31 статьяx:
Alexander Kuznetsov, Yuri Prokhorov, “Rationality over non-closed fields of Fano threefolds with higher geometric Picard rank”, J. Inst. Math. Jussieu, 23:1 (2024), 207–247
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Yuri Prokhorov, “Embeddings of the symmetric groups to the space Cremona group”, Springer Proc. Math. Statist., 409 (2023), 749–762
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Ivan Cheltsov, Adrien Dubouloz, Takashi Kishimoto, “Toric G-solid Fano threefolds”, Sel. Math. New Ser., 29:2 (2023)
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Ivan Cheltsov, “Kummer quartic double solids”, Rend. Circ. Mat. Palermo, II. Ser, 72:3 (2023), 1993
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Ю. Г. Прохоров, “Эквивариантная программа минимальных моделей”, УМН, 76:3 (2021), 93–182; Yu. G. Prokhorov, “Equivariant minimal model program”, Russian Math. Surveys, 76:3 (2021), 461–542
А. А. Кузнецова, “Конечные 3-подгруппы в группе Кремоны ранга 3”, Матем. заметки, 108:5 (2020), 725–749; A. A. Kuznetsova, “Finite 3-Subgroups in the Cremona Group of Rank 3”, Math. Notes, 108:5 (2020), 697–715
Ivan Cheltsov, Alexander Kuznetsov, Konstantin Shramov, “Coble fourfold, S6-invariant quartic threefolds, and Wiman–Edge sextics”, Algebra Number Theory, 14:1 (2020), 213–274
А. А. Авилов, “Бирегулярная и бирациональная геометрия двойных накрытий проективного пространства с ветвлением в квартике с 15 обыкновенными двойными точками”, Изв. РАН. Сер. матем., 83:3 (2019), 5–14; A. Avilov, “Biregular and birational geometry of quartic double solids with 15 nodes”, Izv. Math., 83:3 (2019), 415–423
Ivan Cheltsov, Victor Przyjalkowski, Constantin Shramov, “Burkhardt Quartic, Barth Sextic, and the Icosahedron”, Int. Math. Res. Not. IMRN, 2019:12 (2019), 3683–3703
Ю. Г. Прохоров, “Рациональность трехмерных многообразий Фано с терминальными горенштейновыми особенностями. I”, Труды МИАН, 307 (2019), 230–253; Yuri G. Prokhorov, “Rationality of Fano Threefolds with Terminal Gorenstein Singularities. I”, Proc. Steklov Inst. Math., 307 (2019), 210–231
Ivan Cheltsov, Victor Przyjalkowski, Constantin Shramov, “Which quartic double solids are rational?”, J. Algebraic Geom., 28:2 (2019), 201–243
Artem Avilov, “Automorphisms of singular three-dimensional cubic hypersurfaces”, European Journal of Mathematics, 4:3 (2018), 761
Yuri Prokhorov, Constantin Shramov, “p-subgroups in the space Cremona group”, Math. Nachr., 291:8 (2018), 1374–1389
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