Geodesic
ON CONJUGACY CLASSES OF THE KLEIN SIMPLE GROUP IN CREMONA GROUP
Glasgow mathematical journal, Tome 59 (2017) no. 2, pp. 395-400

Voir la notice de l'article provenant de la source Cambridge University Press

We consider countably many three-dimensional PSL2( $\mathbb{F}$ 7)-del Pezzo surface fibrations over P1. Conjecturally, they are all irrational except two families, one of which is the product of a del Pezzo surface with P1. We show that the other model is PSL2( $\mathbb{F}$ 7)-equivariantly birational to P2×P1. Based on a result of Prokhorov, we show that they are non-conjugate as subgroups of the Cremona group Cr3(C). 
AHMADINEZHAD, HAMID. ON CONJUGACY CLASSES OF THE KLEIN SIMPLE GROUP IN CREMONA GROUP. Glasgow mathematical journal, Tome 59 (2017) no. 2, pp. 395-400. doi: 10.1017/S0017089516000239
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[1] 1. Ahmadinezhad, H., Singular del Pezzo fibrations and birational rigidity, in Automorphisms in birational and affine geometry, Springer Proceedings in Mathematics & Statistics, vol. 79 (Ivan, C., Ciro, C., Hubert, F., James, M., Yuri, G. P., Mikhail, Z., Editors) (Springer International Publishing, Switzerland, 2014), 3–15. Google Scholar

[2] 2. Beauville, A., p-elementary subgroups of the Cremona group, J. Algebra 314 (2) (2007), 553–564. Google Scholar | DOI

[3] 3. Belousov, G., Log del Pezzo surfaces with simple automorphism groups, Proc. Edinb. Math. Soc. (2) 58 (1) (2015), 33–52. Google Scholar

[4] 4. Bogomolov, F. and Prokhorov, Y., On stable conjugacy of finite subgroups of the plane Cremona group, I, Cent. Eur. J. Math. 11 (12) (2013), 2099–2105. Google Scholar

[5] 5. Cheltsov, I., Two local inequalities, Izv. Ross. Akad. Nauk Ser. Mat. 78 (2) (2014), 167–224. Google Scholar

[6] 6. Cheltsov, I. and Shramov, C., Three embeddings of the Klein simple group into the Cremona group of rank three, Transform. Groups 17 (2) (2012), 303–350. Google Scholar | DOI

[7] 7. Cheltsov, I. and Shramov, C., Five embeddings of one simple group, Trans. Amer. Math. Soc. 366 (3) (2014), 1289–1331. Google Scholar | DOI

[8] 8. Grinenko, M., On the birational rigidity of some pencils of del Pezzo surfaces, J. Math. Sci. (New York) 102 (2) (2000), 3933–3937, Algebraic geometry, 10. MR 1794170 (2001j:14012) Google Scholar | DOI

[9] 9. Prokhorov, Y., Simple finite subgroups of the Cremona group of rank 3, J. Algebr. Geom. 21 (3) (2012), 563–600. Google Scholar

[10] 10. Prokhorov, Y., On stable conjugacy of finite subgroups of the plane Cremona group, II, Michigan Math. J., 64 (2) (2015), 293–318. Google Scholar

[11] 11. Pukhlikov, A., Birationally rigid varieties, Mathematical surveys and monographs, vol. 190 (American Mathematical Society, Providence, RI, 2013). Google Scholar

[12] 12. Serre, J.-P., 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), 193–208, back matter. Google Scholar

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