Abstract
We classify quasi-simple finite groups of essential dimension 3.
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D. Abramovich and J. Wang, “Equivariant resolution of singularities in characteristic 0,” Math. Res. Lett., 4, No. 2-3, 427–433 (1997).
A. Beauville, “Finite simple groups of small essential dimension,” in Trends in Contemporary Mathematics. Selected Talks Based on the Presentations at the INdAM Day, June 18, 2014, Springer, Cham (2014), pp. 221–228.
G. Belousov, “Log del Pezzo surfaces with simple automorphism groups,” Proc. Edinburgh Math. Soc., II. Ser., 58, No. 1, 33–52 (2015).
J. Buhler and Z. Reichstein, “On the essential dimension of a finite group,” Compos. Math., 106, No. 2, 159–179 (1997).
I. A. Cheltsov, “Two local inequalities,” Izv. Math., 78, No. 2, 375–426 (2014).
J. H. Conway, R. T. Curtis, S. P. Norton, R. A. Parker, and R. A. Wilson, Atlas of Finite Groups. Maximal Subgroups and Ordinary Characters for Simple Groups, Clarendon Press, Oxford (1985).
I. V. Dolgachev and V. A. Iskovskikh, “Finite subgroups of the plane Cremona group,” in: Algebra, Arithmetic, and Geometry: in Honor of Yu. I. Manin, Vol. I, Progr. Math., Vol. 269, Birkhäuser, Boston (2009), pp. 443–548.
A. Duncan, “Essential dimensions of A7 and S7,” Math. Res. Lett., 17, No. 2, 263–266 (2010).
A. Duncan, “Finite groups of essential dimension 2,” Comment. Math. Helv., 88, No. 3, 555–585 (2013).
G. Karpilovsky, Group Representations, Vol. 2, North-Holland Math. Stud., Vol. 177, North-Holland, Amsterdam (1993).
N. Karpenko and A. Merkurjev, “Essential dimension of finite p-groups,” Invent. Math., 172, 491–508 (2008).
J. Kollár and E. Szabó, “Fixed points of group actions and rational maps,” Canad. J. Math., 52, No. 5, 1054–1056 (2000).
Yu. Prokhorov, “Simple finite subgroups of the Cremona group of rank 3,” J. Algebraic Geom., 21, No. 3, 563–600 (2012).
Yu. Prokhorov. “On G-Fano threefolds,” Izv. Ross. Akad. Nauk Ser. Mat., 79, No. 4, 159–174 (2015).
Yu. Prokhorov and C. Shramov, Finite Groups of Birational Selfmaps of Threefolds, arXiv:1611.00789 (2016).
Yu. Prokhorov and C. Shramov, Jordan Constant for Cremona Group of Rank 3, arXiv:1608.00709 (2016).
Yu. Prokhorov and C. Shramov, p-Subgroups in the Space Cremona Group, arXiv:1610.02990 (2016).
J.-P. Serre, “Le groupe de Cremona et ses sous-groupes finis,” in: Séminaire Bourbaki. Volume 2008/2009. Exposés 997–1011, Soc. Math. de France, Paris (2010), pp. 75–100.
V. I. Tsygankov, “The conjugacy classes of finite nonsolvable subgroups in the plane Cremona group,” Adv. Geom., 13, No. 2, 323–347 (2013).
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In memory of Professor Alfred Lvovich Shmel’kin
Translated from Fundamentalnaya i Prikladnaya Matematika, Vol. 22, No. 4, pp. 189–199, 2019.
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Prokhorov, Y. Quasi-Simple Finite Groups of Essential Dimension 3. J Math Sci 257, 876–882 (2021). https://doi.org/10.1007/s10958-021-05527-8
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DOI: https://doi.org/10.1007/s10958-021-05527-8