Abstract
Let G be a solvable subgroup of the automorphism group Aut(X) of
a compact Kahler manifold X of complex dimension n, and let N(G) be
the normal subgroup of G consisting of elements with null entropy. Let
us denote by G^* the image of G under the natural map from Aut(X)
to GL(V,R), where V is the Dolbeault cohomology group H^{1,1}(X,R).
Assume that the Zariski closure of G^* in GL(V_C) is connected. In this
paper we show that G=N(G) is a free abelian group of rank r(G) \leq
n - 1 and that the rank estimate is optimal. This gives a proof of
the conjecture of Tits type. Our approach also gives some non-obvious
implications on the structure of solvable subgroups of automorphisms
of a compact Kahler manifold that are analogous to abelian subgroups
of automorphisms. Moreover, if the rank r(G) of the quotient group
G=N(G) is equal to n - 1 and the identity component of Aut(X) is
trivial, then it will be shown by using a theorem of Lieberman that
N(G) is a finiite set.
Preprints
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