We classify compact complex surfaces whose groups of bimeromorphic selfmaps have bounded finite subgroups. We also prove that the stabilizer of a point in the automorphism group of a compact complex surface of zero Kodaira dimension, as well as the stabilizer of a point in the automorphism group of an arbitrary compact Khler manifold of nonnegative Kodaira dimension, always has bounded finite subgroups.

Bibliography: 23 titles.

中文翻译：

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紧致复杂曲面的有界自同构群

我们对紧致的复杂曲面进行分类，这些曲面的双美态自映射组具有有限的子组。我们还证明了零Kodaira尺寸的紧致复杂曲面的自同构群中的一个点的稳定器，以及非负Kodaira尺寸的任意紧致Khler流形的自同构群中的一个点的稳定器，总是有界有限亚组。

参考书目：23种。