Mots-clés : Kähler manifold, bimeromorphic map
@article{SM_2023_214_1_a1,
author = {A. S. Golota},
title = {Jordan property for groups of bimeromorphic automorphisms of compact {K\"ahler} threefolds},
journal = {Sbornik. Mathematics},
pages = {28--38},
year = {2023},
volume = {214},
number = {1},
language = {en},
url = {http://geodesic.mathdoc.fr/item/SM_2023_214_1_a1/}
}
A. S. Golota. Jordan property for groups of bimeromorphic automorphisms of compact Kähler threefolds. Sbornik. Mathematics, Tome 214 (2023) no. 1, pp. 28-38. http://geodesic.mathdoc.fr/item/SM_2023_214_1_a1/
[1] J. Déserti, The Cremona group and its subgroups, Math. Surveys Monogr., 252, Amer. Math. Soc., Providence, RI, 2021, xii+187 pp. | DOI | MR | Zbl
[2] C. Jordan, “Mémoire sur les équations différentielles linéaires à intégrale algébrique”, J. Reine Angew. Math., 1878:84 (1878), 89–215 | DOI | MR | Zbl
[3] 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
[4] S. Meng and D.-Q. Zhang, “Jordan property for non-linear algebraic groups and projective varieties”, Amer. J. Math., 140:4 (2018), 1133–1145 | DOI | MR | Zbl
[5] 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
[6] 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
[7] 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
[8] 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
[9] Yu. G. Zarhin, “Theta groups and products of abelian and rational varieties”, Proc. Edinb. Math. Soc. (2), 57:1 (2014), 299–304 | DOI | MR | Zbl
[10] Yu. Prokhorov and C. Shramov, “Jordan property for groups of birational selfmaps”, Compos. Math., 150:12 (2014), 2054–2072 | DOI | MR | Zbl
[11] Yu. Prokhorov and C. Shramov, “Jordan property for Cremona groups”, Amer. J. Math., 138:2 (2016), 403–418 | DOI | MR | Zbl
[12] Yu. Prokhorov and C. Shramov, “Automorphism groups of compact complex surfaces”, Int. Math. Res. Not. IMRN, 2021:14 (2021), 10490–10520 | DOI | MR | Zbl
[13] Yu. Prokhorov and C. Shramov, “Finite groups of birational selfmaps of threefolds”, Math. Res. Lett., 25:3 (2018), 957–972 | DOI | MR | Zbl
[14] Yu. G. Prokhorov and C. A. Shramov, “Finite groups of bimeromorphic selfmaps 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
[15] Yu. G. Prokhorov and C. A. Shramov, “Finite groups of bimeromorphic selfmaps of nonuniruled Kähler threefolds”, Mat. Sb., 213:12 (2022), 86–108 ; English transl. in Sb. Math., 213:12 (2022), 1695-1714 | DOI | DOI
[16] 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
[17] A. Höring and T. Peternell, “Minimal models for Kähler threefolds”, Invent. Math., 203:1 (2016), 217–264 | DOI | MR | Zbl
[18] C. W. Curtis and I. Reiner, Representation theory of finite groups and associative algebras, Pure Appl. Math., XI, Interscience Publishers (a division of John Wiley Sons), New York–London, 1962, xiv+685 pp. | MR | Zbl
[19] R. Elkik, “Rationalité des singularites canoniques”, Invent. Math., 64:1 (1981), 1–6 | DOI | MR | Zbl
[20] J. Kollár and Sh. Mori, Birational geometry of algebraic varieties, With the collaboration of C. H. Clemens and A. Corti, Cambridge Tracts in Math., 134, Cambridge Univ. Press, Cambridge, 1998, viii+254 pp. | DOI | MR | Zbl
[21] S. Boucksom, “Divisorial Zariski decompositions on compact complex manifolds”, Ann. Sci. École Norm. Sup. (4), 37:1 (2004), 45–76 | DOI | MR | Zbl
[22] S. Boucksom, J.-P. Demailly, M. Păun and T. Peternell, “The pseudo-effective cone of a compact Kähler manifold and varieties of negative Kodaira dimension”, J. Algebraic Geom., 22:2 (2013), 201–248 | DOI | MR | Zbl
[23] M. Brunella, “A positivity property for foliations on compact Kähler manifolds”, Internat. J. Math., 17:1 (2006), 35–43 | DOI | MR | Zbl
[24] H. Grauert and R. Remmert, Coherent analytic sheaves, Grundlehren Math. Wiss., 265, Springer-Verlag, Berlin, 1984, xviii+249 pp. | DOI | MR | Zbl
[25] M. Hanamura, “On the birational automorphism groups of algebraic varieties”, Compos. Math., 63:1 (1987), 123–142 | MR | Zbl
[26] J. Kollár, “Flops”, Nagoya Math. J., 113 (1989), 15–36 | DOI | MR | Zbl
[27] J. R. King, “The currents defined by analytic varieties”, Acta Math., 127:3–4 (1971), 185–220 | DOI | MR | Zbl
[28] J. Jia and S. Meng, Moishezon manifolds with no nef and big classes, arXiv: 2208.12013
[29] J. Cao and A. Höring, “Rational curves on compact Kähler manifolds”, J. Differential Geom., 114:1 (2020), 1–39 | DOI | MR | Zbl