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In [Matsusaka, T. Polarized varieties, fields of moduli and generalized Kummer varieties of polarized abelian varieties. Amer. J. Math. 80 1958 45--82.] it is proved that a non-singular projective variety has a maximal algebraic group of automorphisms (that is, every group which acts on the variety by automorphisms contains a maximal algebraic subgroup)