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@article{IM2_2019_83_4_a8, author = {V. L. Popov}, title = {Three plots about {Cremona} groups}, journal = {Izvestiya. Mathematics }, pages = {830--859}, publisher = {mathdoc}, volume = {83}, number = {4}, year = {2019}, language = {en}, url = {http://geodesic.mathdoc.fr/item/IM2_2019_83_4_a8/} }
V. L. Popov. Three plots about Cremona groups. Izvestiya. Mathematics , Tome 83 (2019) no. 4, pp. 830-859. http://geodesic.mathdoc.fr/item/IM2_2019_83_4_a8/
[1] J.-P. Serre, “Le groupe de Cremona et ses sous-groupes finis”, Séminaire Bourbaki, Exposés 997–1011, v. 2008/2009, Astérisque, 332, Soc. Math. France, Paris, 2010, vii, 75–100, Exp. No. 1000 | MR | Zbl
[2] J. Blanc, J.-P. Furter, “Topologies and structures of the Cremona groups”, Ann. of Math. (2), 178:3 (2013), 1173–1198 | DOI | MR | Zbl
[3] V. L. Popov, “Some subgroups of the Cremona groups”, Affine algebraic geometry (Osaka, 2011), World Sci. Publ., Hackensack, NJ, 2013, 213–242 | DOI | MR | Zbl
[4] V. L. Popov, “Tori in the Cremona groups”, Izv. Math., 77:4 (2013), 742–771 | DOI | DOI | MR | Zbl
[5] V. L. Popov, “On infinite dimensional algebraic transformation groups”, Transform. Groups, 19:2 (2014), 549–568 | DOI | MR | Zbl
[6] V. L. Popov, “Borel subgroups of Cremona groups”, Math. Notes, 102:1 (2017), 60–67 | DOI | DOI | MR | Zbl
[7] I. V. Dolgachev, V. A. Iskovskikh, “Finite subgroups of the plane Cremona group”, Algebra, arithmetic, and geometry, In honor of Yu. I. Manin, v. I, Progr. Math., 269, Birkhäuser Boston, Inc., Boston, MA, 2009, 443–548 | DOI | MR | Zbl
[8] V. L. Popov, “Jordan groups and automorphism groups of algebraic varieties”, Automorphisms in birational and affine geometry (Levico Terme, 2012), Springer Proc. Math. Stat., 79, Springer, Cham, 2014, 185–213 | DOI | MR | Zbl
[9] V. L. Popov, Cremona conference–Basel 2016, Question session, 2016 https://algebra.dmi.unibas.ch/blanc/cremonaconference/index.html
[10] J.-P. Serre, “A Minkowski-style bound for the orders of the finite subgroups of the Cremona group of rank 2 over an arbitrary field”, Mosc. Math. J., 9:1 (2009), 183–198 | MR | Zbl
[11] Yu. Prokhorov, C. Shramov, “Jordan property for Cremona groups”, Amer. J. Math., 138:2 (2016), 403–418 | DOI | MR | Zbl
[12] C. Birkar, Birational geometry of algebraic varieties, 2018, arXiv: 1801.00013
[13] S. Cantat, “Morphisms between Cremona groups, and characterization of rational varieties”, Compositio Math., 150:7 (2014), 1107–1124 | DOI | MR | Zbl
[14] J. Blanc, S. Zimmermann, “Topological simplicity of the Cremona groups”, Amer. J. Math., 140:5 (2018), 1297–1309 ; (2015), arXiv: 1511.08907 | DOI | MR | Zbl
[15] J. Blanc, “Groupes de Cremona, connexité et simplicité”, Ann. Sci. Éc. Norm. Supér. (4), 43:2 (2010), 357–364 | DOI | MR | Zbl
[16] J. W. Alexander, “On the deformation of an $n$-cell”, Proc. Nat. Acad. Sci. USA, 9:12 (1923), 406–407 | DOI | Zbl
[17] I. R. Shafarevich, “On some infinite-dimensional groups. II”, Math. USSR-Izv., 18:1 (1982), 185–194 | DOI | MR | Zbl
[18] M. Rosenlicht, “Some basic theorems on algebraic groups”, Amer. J. Math., 78:2 (1956), 401–443 | DOI | MR | Zbl
[19] E. Bierstone, P. D. Milman, “Canonical desingularization in characteristic zero by blowing up the maximum strata of a local invariant”, Invent. Math., 128:2 (1997), 207–302 | DOI | MR | Zbl
[20] V. L. Popov, E. B. Vinberg, “Invariant theory”, Algebraic geometry IV, Encyclopaedia Math. Sci., 55, Springer-Verlag, Berlin, 1994, 123–278 | DOI | MR | MR | Zbl | Zbl
[21] Z. Reichstein, “On the notion of essential dimension for algebraic groups”, Transform. Groups, 5:3 (2000), 265–304 | DOI | MR | Zbl
[22] Z. Reichstein, “Compressions of group actions”, Invariant theory in all characteristics, CRM Proc. Lecture Notes, 35, Amer. Math. Soc., Providence, RI, 2004, 199–202 | DOI | MR | Zbl
[23] M. Garcia-Armas, “Strongly incompressible curves”, Canad. J. Math., 68:3 (2016), 541–570 | DOI | MR | Zbl
[24] I. R. Shafarevich, Basic algebraic geometry, v. 1, Varieties in projective space, 3rd ed., Springer, Heidelberg, 2013, xviii+310 pp. ; v. 2, Schemes and complex manifolds, 3rd ed., 2013, xiv+262 pp. | DOI | DOI | MR | MR | MR | Zbl | Zbl | Zbl
[25] B. L. van der Varden, Algebra, 2-e izd., Nauka, M., 1979, 624 pp. ; B. L. van der Waerden, Algebra, v. I, Heidelberger Taschenbücher, 12, 8. Aufl., Springer-Verlag, Berlin–New York, 1971, ix+272 pp. ; v. II, Heidelberger Taschenbücher, 23, 5. Aufl., 1967, x+300 pp. ; B. L. van der Waerden, Algebra, Reprint. from the English transl. of 1970, т. 1, 2, Springer-Verlag, New York, 1991, xiv+265 pp., xii+284 с. | MR | Zbl | MR | Zbl | MR | Zbl | MR | MR | Zbl
[26] T. A. Springer, “Poincaré series of binary polyhedral groups and McKay's correspondence”, Math. Ann., 278:1-4 (1987), 99–116 | DOI | MR | Zbl
[27] N. Lemire, V. L. Popov, Z. Reichstein, “Cayley groups”, J. Amer. Math. Soc., 19:4 (2006), 921–967 | DOI | MR | Zbl
[28] I. Dolgachev, A. Duncan, “Fixed points of a finite subgroup of the plane Cremona group”, Algebr. Geom., 3:4 (2016), 441–460 | DOI | MR | Zbl
[29] K. A. Nguyen, M. van der Put, J. Top, “Algebraic subgroups of $\operatorname{GL}_2(\mathbb C)$”, Indag. Math. (N.S.), 19:2 (2008), 287–297 | DOI | MR | Zbl
[30] J. Blanc, Finite Abelian subgroups of the Cremona group of the plane, Ph.D. thèse No. 3777, Univ. Genève, Genève, 2006, 186 pp., arXiv: math/0610368
[31] S. Lang, Algebra, Addison-Wesley Publishing Co., Inc., Reading, Mass., 1965, xvii+508 pp. | MR | Zbl | Zbl
[32] J. Buhler, Z. Reichstein, “On the essential dimension of a finite group”, Compositio Math., 106:2 (1997), 159–179 | DOI | MR | Zbl
[33] Z. Reichstein, B. Youssin, “Essential dimensions of algebraic groups and a resolution theorem for $G$-varieties”, Canad. J. Math., 52:5 (2000), 1018–1056 | DOI | MR | Zbl
[34] E. B. Vinberg, Linear representations of groups, Basler Lehrbücher, 2, Birkhäuser Verlag, Basel, 1989, iv+146 pp. | DOI | MR | MR | Zbl | Zbl
[35] V. L. Popov, “On the Makar-Limanov, Derksen invariants, and finite automorphism groups of algebraic varieties”, Affine algebraic geometry, The Russell festschrift, CRM Proc. Lecture Notes, 54, Amer. Math. Soc., Providence, RI, 2011, 289–311 | DOI | MR | Zbl
[36] Yu. Prokhorov, C. Shramov, “Jordan constant for Cremona group of rank $3$”, Mosc. Math. J., 17:3 (2017), 457–509 | MR
[37] Ch. Urech, Letter of October 11, 2018 to V. L. Popov, 2018
[38] J. Blanc, S. Lamy, S. Zimmermann, Quotients of higher dimensional Cremona groups, 2019, 84 pp., arXiv: 1901.04145v2
[39] J. Déserti, “Le groupe de Cremona est hopfien”, C. R. Math. Acad. Sci. Paris, 344:3 (2007), 153–156 | DOI | MR | Zbl
[40] L. N. Mann, J. C. Su, “Actions of elementary $p$-groups on manifolds”, Trans. Amer. Math. Soc., 106 (1963), 115–126 | DOI | MR | Zbl
[41] A. Borisov, Letters of May $1$ and $2$, 2017 to V. L. Popov, 2017