Bott–Chern blow-up formulae and the bimeromorphic invariance of the ∂∂̄-Lemma for threefolds

Yang, Song; Yang, Xiangdong

doi:10.1090/tran/8213

Bott–Chern blow-up formulae and the bimeromorphic invariance of the $\partial \bar {\partial }$-Lemma for threefolds
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by Song Yang and Xiangdong Yang PDF

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Abstract:

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-Kählerness 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.

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