Finite groups of bimeromorphic self-maps of nonuniruled Kähler threefolds
Sbornik. Mathematics, Tome 213 (2022) no. 12, pp. 1695-1714 Cet article a éte moissonné depuis la source Math-Net.Ru

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We prove the Jordan property for groups of bimeromorphic self-maps of three-dimensional compact Kähler varieties of nonnegative Kodaira dimension and positive irregularity. Bibliography: 32 titles.
Keywords: group of bimeromorphic self-maps, Kähler variety.
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Yu. G. Prokhorov; С. A. Shramov. Finite groups of bimeromorphic self-maps of nonuniruled Kähler threefolds. Sbornik. Mathematics, Tome 213 (2022) no. 12, pp. 1695-1714. http://geodesic.mathdoc.fr/item/SM_2022_213_12_a4/

[1] V. L. Popov, “On the Makar-Limanov, Derksen invariants, and finite automorphism groups of algebraic varieties”, Affine algebraic geometry, The Russell festschrift (McGill Univ., Montreal, QC 2009), CRM Proc. Lecture Notes, 54, Amer. Math. Soc., Providence, RI, 2011, 289–311 | DOI | MR | Zbl

[2] Yu. Prokhorov and C. Shramov, “Automorphism groups of compact complex surfaces”, Int. Math. Res. Not. IMRN, 2021:14 (2021), 10490–10520 | DOI | MR | Zbl

[3] V. L. Popov, “The Jordan property for Lie groups and automorphism groups of complex spaces”, Math. Notes, 103:5 (2018), 811–819 | DOI | MR | Zbl

[4] J. H. Kim, “Jordan property and automorphism groups of normal compact Kähler varieties”, Commun. Contemp. Math., 20:3 (2018), 1750024, 9 pp. | DOI | MR | Zbl

[5] S. Meng, F. Perroni and D.-Q. Zhang, “Jordan property for automorphism groups of compact spaces in Fujiki's class $\mathscr{C}$”, J. Topol., 15:2 (2022), 806–814 ; arXiv: 2011.09381 | DOI | MR

[6] Yu. G. Prokhorov and C. A. Shramov, “Automorphism groups of Moishezon threefolds”, Mat. Zametki, 106:4 (2019), 636–640 ; English transl. in Math. Notes, 106:4 (2019), 651–655 | DOI | MR | Zbl | DOI

[7] Yu. G. Prokhorov and K. A. Shramov (C. A. Shramov), “Finite groups of bimeromorphic self-maps of uniruled Kähler threefolds”, Izv. Ross. Akad. Nauk Ser. Mat., 84:5 (2020), 169–196 ; English transl. in Izv. Math., 84:5 (2020), 978–1001 | DOI | MR | Zbl | DOI

[8] T. Bandman and Yu. G. Zarhin, “Bimeromorphic automorphism groups of certain $\mathbb{P}^1$-bundles”, Eur. J. Math., 7 (2021), 641–670 | DOI | MR | Zbl

[9] T. Bandman and Yu. G. Zarhin, Automorphism groups of $\mathbb{P}^1$-bundles over a non-uniruled base, arXiv: 2103.07015

[10] T. Bandman and Yu. G. Zarhin, Simple complex tori of algebraic dimension $0$, arXiv: 2106.10308

[11] Yu. G. Zarhin, “Complex tori, theta groups and their Jordan properties”, Algebra, number theory, and algebraic geometry, Tr. Mat. Inst. Steklova, 307, Steklov Mathematical Institute of RAS, Moscow, 2019, 32–62 ; English transl. in Proc. Steklov Inst. Math., 307 (2019), 22–50 | DOI | MR | Zbl | DOI

[12] A. Höring and Th. Peternell, “Minimal models for Kähler threefolds”, Invent. Math., 203:1–2 (2016), 217–264 | DOI | MR | Zbl

[13] M. Brunella, “A positivity property for foliations on compact Kähler manifolds”, Internat. J. Math., 17:1 (2006), 35–43 | DOI | MR | Zbl

[14] J.-P. Demailly and Th. Peternell, “A Kawamata-Viehweg vanishing theorem on compact Kähler manifolds”, J. Differential Geom., 63:2 (2003), 231–277 | DOI | MR | Zbl

[15] Yu. Prokhorov and C. Shramov, “Jordan property for groups of birational self-maps”, Compos. Math., 150:12 (2014), 2054–2072 | DOI | MR | Zbl

[16] Yu. G. Prokhorov, “Equivariant minimal model program”, Uspekhi Mat. Nauk, 76:3(459) (2021), 93–182 ; English transl. in Russian Math. Surveys, 76:3 (2021), 461–542 | DOI | MR | Zbl | DOI

[17] A. Fujiki, “A theorem on bimeromorphic maps of Kähler manifolds and its applications”, Publ. Res. Inst. Math. Sci., 17:2 (1981), 735–754 | DOI | MR | Zbl

[18] A. Golota, Jordan property for groups of bimeromorphic automorphisms of compact Kähler threefolds, arXiv: 2112.02673

[19] K. Ueno, Classification theory of algebraic varieties and compact complex spaces, Notes written in collaboration with P. Cherenack, Lecture Notes in Math., 439, Springer-Verlag, Berlin–New York, 1975, xix+278 pp. | DOI | MR | Zbl

[20] M. Reid, “Canonical 3-folds”, Journées de géometrie algébrique (Angers 1979), Sijthoff Noordhoff, Alphen aan den Rijn–Germantown, MD, 1980, 273–310 | MR | Zbl

[21] J. Kollár and Sh. Mori, Birational geometry of algebraic varieties, With the collaboration of C. H. Clemens, A. Corti, Cambridge Tracts in Math., 134, Cambridge Univ. Press, Cambridge, 1998, viii+254 pp. | DOI | MR | Zbl

[22] J.-P. Serre, “Bounds for the orders of the finite subgroups of $G(k)$”, Group representation theory, EPFL Press, Lausanne, 2007, 405–450 | MR | Zbl

[23] C. Birkenhake and H. Lange, Complex abelian varieties, Grundlehren Math. Wiss., 302, 2nd ed., Springer-Verlag, Berlin, 2004, xii+635 pp. | DOI | MR | Zbl

[24] P. Graf, “Algebraic approximation of Kähler threefolds of Kodaira dimension zero”, Math. Ann., 371:1–2 (2018), 487–516 | DOI | MR | Zbl

[25] Yu. G. Prokhorov and C. A. Shramov, “Bounded automorphism groups of compact complex surfaces”, Mat. Sb., 211:9 (2020), 105–118 ; English transl. in Sb. Math., 211:9 (2020), 1310–1322 | DOI | MR | Zbl | DOI

[26] V. V. Shokurov, “3-fold log flips”, Izv. Ross. Akad. Nauk Ser. Mat., 56:1 (1992), 105–203 ; English transl. in Izv. Math., 40:1 (1993), 95–202 | MR | Zbl | DOI

[27] J. Wang, “On the Iitaka conjecture $C_{n,m}$ for Kähler fibre spaces”, Ann. Fac. Sci. Toulouse Math. (6), 30:4 (2021), 813–897 | DOI | MR | Zbl

[28] J. Kollár, “Flops”, Nagoya Math. J., 113 (1989), 15–36 | DOI | MR | Zbl

[29] N. Nakayama, “The lower semi-continuity of the plurigenera of complex varieties”, Algebraic geometry (Sendai 1985), Adv. Stud. Pure Math., 10, North-Holland, Amsterdam, 1987, 551–590 | DOI | MR | Zbl

[30] Vik. S. Kulikov, “Decomposition of a birational map of three-dimensional varieties outside codimension 2”, Izv. Akad. Nauk SSSR Ser. Mat., 46:4 (1982), 881–895 ; English transl. in Izv. Math., 21:1 (1983), 187–200 | MR | Zbl | DOI

[31] W. P. Barth, K. Hulek, C. A. M. Peters and A. Van de Ven, Compact complex surfaces, Ergeb. Math. Grenzgeb. (3), 4, 2nd ed., Springer-Verlag, Berlin, 2004, xii+436 pp. | DOI | MR | Zbl

[32] J. Varouchas, “Kähler spaces and proper open morphisms”, Math. Ann., 283:1 (1989), 13–52 | DOI | MR | Zbl