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Automorphism groups of Moishezon threefolds. (English. Russian original) Zbl 1433.14039

Math. Notes 106, No. 4, 651-655 (2019); translation from Mat. Zametki 106, No. 4, 636-640 (2019).
A group \(G\) has Jordan property if there is constant \(J\) such that every finite subgroup of \(G\) has an abelian subgroup of index \(\leq J\). It is known that the birational transformation group of a rationally connected complex algebraic variety has Jordan property. In this short paper the authors show that the automorphism groups of three dimensional compact Moishezon spaces satisfy Jordan property. We recall that Moishezon spaces are complex spaces that are bimeromorphic to algebraic varieties.

MSC:

14J50 Automorphisms of surfaces and higher-dimensional varieties
14J30 \(3\)-folds
14E07 Birational automorphisms, Cremona group and generalizations
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[1] V. L. Popov, in Affine Algebraic Geometry, CRM Proc. Lecture Notes (Amer. Math. Soc., Providence, RI, 2011), Vol. 54, pp. 289-311.
[2] Curtis, Ch W.; Reiner, I., Representation Theory of Finite Groups and Associative Algebras (1962), New York · Zbl 0131.25601
[3] Yu. Prokhorov and C. Shramov, Amer. J. Math. 138 (2), 403 (2016).
[4] C. Birkar, Singularities of Linear Systems and Boundedness of Fano Varieties, arXiv: 1609.05543 (2016). · Zbl 1348.14037
[5] Prokhorov, Yu; Shramov, C., No article title, Compos. Math, 150, 2054 (2014) · Zbl 1314.14022
[6] I. Mundet i Riera, Finite Group Actions on Homology Spheres and Manifolds with Nonzero Euler Characteristic, arXiv: 1403.0383 (2014). · Zbl 1342.57021
[7] I. Mundet i Riera, Finite Group Actions on Manifolds Without Odd Cohomology, arXiv: 1310.6565 (2013). · Zbl 1342.57021
[8] Meng, Sh; Zhang, D-Q, No article title, Amer. J. Math, 140, 1133 (2018) · Zbl 1428.14023
[9] J. H. Kim, Commun. Contemp. Math. 20, 1750024 (2018). · Zbl 1400.14108
[10] Zarhin, Yu G., No article title, Proc. Edinb. Math. Soc. (2), 57, 299 (2014) · Zbl 1311.14018
[11] B. Csikós, L. Pyber, and E. Szabó, Diffeomorphism Groups of Compact 4-Manifolds are not Always Jordan, arXiv: 1411.7524 (2014).
[12] Prokhorov, Yu; Shramov, C., No article title, Math. Res. Lett, 25, 957 (2018) · Zbl 1423.14094
[13] Yu. Prokhorov and C. Shramov, Automorphism Groups of Compact Complex Surfaces, Int. Math. Res. Notices, arXiv: https://doi.org/10.1093/imrn/rnz124 and https://arxiv.org/abs/1708.03566 (2017). · Zbl 1411.14018
[14] Moishezon, B. G., No article title, Izv. Akad. Nauk SSSR Ser. Mat, 30, 133 (1966)
[15] Moishezon, B. G., No article title, Izv. Akad. Nauk SSSR Ser. Mat, 30, 345 (1966)
[16] Several Complex Variables VII. Sheaf-Theoretical Methods in Complex Analysis, Ed. by H. Grauert, Th. Peternell, R. Remmert, R. V. Gamkrelidze, in Encyclopaedia of Mathematical Sciences (SpringerVerlag, Berlin, 1994), Vol. 74. · Zbl 0793.00010
[17] Barth, W. P.; Hulek, K.; Peters, Ch A. M.; Ven, A., Compact Complex Surfaces (2004), Berlin · Zbl 1036.14016
[18] Moishezon, B. G., No article title, Izv. Akad. Nauk SSSR Ser. Mat, 30, 621 (1966)
[19] Kollár, J., Rational Curves on Algebraic Varieties (1996), Berlin
[20] Bierstone, E.; Milman, P. D., No article title, Invent. Math, 128, 207 (1997) · Zbl 0896.14006
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