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Regular version of the site

Article

Tori in the Cremona groups

Izvestiya. Mathematics. 2013. Vol. 77. No. 4. P. 742-771.

We classify up to conjugacy the subgroups of certain types in the full, affine, and special affine Cremona groups.
We prove that the normalizers of these subgroups are algebraic. As an application, we obtain new results in the linearization problem by generalizing Bia{\l}ynicki-Birula's results  of 1966--67 to disconnected groups.
 We prove fusion theorems for  n-dimensional tori in the affine and in special affine Cremona groups of rank  n  and introduce and discuss  the notions of Jordan decomposition and torsion prime numbers for the Cremona groups.