It is conjectured that the Dolbeault cohomology of a complex nilmanifold $X$ is computed by left-invariant forms. We prove this under the assumption that $X$ is suitably foliated in toroidal groups and deduce that the conjecture holds in real dimension up to six. Our approach generalizes previous methods, where the existence of a holomorphic fibration was a crucial ingredient.

中文翻译：

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复杂环状环中的复杂尼马尔道勒的Dolbeault同调

可以推测，复杂的nilmanifold $ X $的Dolbeault同调是通过左不变形式计算的。我们在这样的假设下证明了这一点，即$ X $适当地叶状排列在环形组中，并推论该猜想在实际维数中最多可容纳6个。我们的方法概括了以前的方法，其中全态纤维化的存在是关键因素。