# Journal of the Ramanujan Mathematical Society

Volume 28A, Issue SPL, July – Special Issue 2013 pp. 41–54.

On connected automorphism groups of algebraic varieties**Authors**: Michel Brion

**Author institution:**Institut Fourier, B. P. 74, 38402 Saint-Martin d'Hères Cedex, France

**Summary:**Let X be a normal projective algebraic variety, G its largest connected automorphism group, and A(G) the Albanese variety of G. We determine the isogeny class of A(G) in terms of the geometry of X. In characteristic 0, we show that the dimension of A(G) is the rank of every maximal trivial direct summand of the tangent sheaf of X. Also, we obtain an optimal bound for the dimension of the largest anti-affine closed subgroup of G (which is the smallest closed subgroup that maps onto A(G)).

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