Compact Kähler manifolds with automorphism groups of maximal rank

For an automorphism group G on an n-dimensional (n > 2) normal projective variety or a compact Kähler manifold X so that G modulo its subgroup N(G) of null entropy elements is an abelian group of maximal rank n-1, we show that N(G) is virtually contained in Aut_0(X), the X is a quotient of a complex torus T and G is mostly descended from the symmetries on the torus T, provided that both X and the pair (X, G) are minimal.

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