The purpose of this paper is to study the bimeromorphic invariants of compact complex manifolds in terms of Bott-Chern cohomology. We prove a blow-up formula for Bott-Chern cohomology. As an application, we show that for compact complex threefolds the non-Kahlerness degrees, introduced by Angella-Tomassini [Invent. Math. 192, (2013), 71-81], are bimeromorphic invariants. Consequently, the $\partial\bar{\partial}$-Lemma on threefolds admits the bimeromorphic invariance.

中文翻译：

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Bott-Chern 爆炸公式和 $\partial \overline {\partial }$-Lemma for 三重的双同胚不变性

本文的目的是根据 Bott-Chern 上同调研究紧复流形的双同胚不变量。我们证明了 Bott-Chern 上同调的爆破公式。作为一个应用，我们展示了由 Angella-Tomassini [Invent. 数学。192, (2013), 71-81]，是双同态不变量。因此，三重上的 $\partial\bar{\partial}$-Lemma 承认双同胚不变性。