We show that every compact complex analytic space endowed with a fine logarithmic structure and every morphism between such spaces admit a semi-universal deformation. These results generalize the analogous results in complex analytic geometry first independently proved by A. Douady and H. Grauert in the ’70. We follow Douady’s two steps process approach consisting of an infinite-dimensional construction of the deformation space followed by a finite-dimensional reduction.

中文翻译：

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对数复几何中的解析半万能变形

我们表明，每个紧致的复解析空间都具有精细的对数结构，并且这些空间之间的每个态射都允许半万有变形。这些结果推广了 A. Douady 和 H. Grauert 在 70 年代首次独立证明的复解析几何中的类似结果。我们遵循 Douady 的两步过程方法，包括变形空间的无限维构造，然后是有限维缩减。