包含大自同构可解群的紧致Kähler流形
Compact Kähler manifolds admitting large solvable groups of automorphisms
摘要：
设G是n维紧致Kähler流形X的自同构自同构群，N（G）是零熵元的子集.设G不存在非交换自由子群。改进了已知的Tits方法，得到了直到用有限指数子群代替G，G/N（G）是秩< n-1的自由阿尔贝群，或G/N（G）是秩n-1的自由阿尔贝群且X是复环面，或G是秩n-1的自由阿尔贝群.如果最后一种情况发生，则X是关于一个阿贝尔簇的商的G-等变双有理，只要X是n > 2维的射影流形并且不是有理连通的。我们还证明并使用了Fujiki和Lieberman关于Aut（X）结构的一个定理的推广。
英文摘要：
Let G be a group of automorphisms of a compact Kähler manifold X of dimension n and N(G) the subset of null-entropy elements. Suppose G admits no non-abelian free subgroup. Improving the known Tits alternative, we obtain that, up to replace G by a finite-index subgroup, either G/N(G) is a free abelian group of rank < n-1, or G/N(G) is a free abelian group of rank n-1 and X is a complex torus, or G is a free abelian group of rank n-1. If the last case occurs, X is G-equivariant birational to the quotient of an abelian variety provided that X is a projective manifold of dimension n > 2 and is not rationally connected. We also prove and use a generalization of a theorem by Fujiki and Lieberman on the structure of Aut(X).
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