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.References
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Additional Information
- Song Yang
- Affiliation: Center for Applied Mathematics, Tianjin University, Tianjin 300072, People’s Republic of China
- MR Author ID: 122624
- Email: syangmath@tju.edu.cn
- Xiangdong Yang
- Affiliation: Department of Mathematics, Chongqing University, Chongqing 401331, People’s Republic of China
- Email: math.yang@cqu.edu.cn
- Received by editor(s): September 22, 2018
- Received by editor(s) in revised form: May 17, 2020
- Published electronically: October 5, 2020
- Additional Notes: This work was partially supported by the National Nature Science Foundation of China (Grants No. 11571242, No. 11701414, and No. 11701051) and the China Scholarship Council.
- © Copyright 2020 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 373 (2020), 8885-8909
- MSC (2010): Primary 32Q55, 32C35; Secondary 32S45
- DOI: https://doi.org/10.1090/tran/8213
- MathSciNet review: 4177279