Geodesic
Tori in the Cremona groups
Izvestiya. Mathematics , Tome 77 (2013) no. 4, pp. 742-771

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We classify up to conjugacy all subgroups of certain types in the full, affine and special affine Cremona groups and prove that the normalizers of these subgroups are algebraic. As an application, we obtain new results on the linearization problem by generalizing Białynicki-Birula's results of 1966–67 to disconnected groups. We prove fusion theorems for $n$-dimensional tori in the affine and special affine Cremona groups of rank $n$, and introduce and discuss the notions of Jordan decomposition and torsion primes for the Cremona groups.
Keywords: Cremona group, algebraic torus, diagonalizable algebraic group, conjugate subgroups, fusion theorems
Mots-clés : affine Cremona group, torsion primes. 
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     author = {V. L. Popov},
     title = {Tori in the {Cremona} groups},
     journal = {Izvestiya. Mathematics },
     pages = {742--771},
     publisher = {mathdoc},
     volume = {77},
     number = {4},
     year = {2013},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/IM2_2013_77_4_a6/}
}
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V. L. Popov. Tori in the Cremona groups. Izvestiya. Mathematics , Tome 77 (2013) no. 4, pp. 742-771. http://geodesic.mathdoc.fr/item/IM2_2013_77_4_a6/