The heredity and bimeromorphic invariance of the $\partial \protect \,\protect \overline{\protect \!\partial }$-lemma property

Lingxu Meng

doi:10.5802/crmath.203

Complex analysis and geometry

The heredity and bimeromorphic invariance of the

\partial \bar{\partial}

-lemma property

Lingxu Meng ¹

¹ Department of Mathematics, North University of China, Taiyuan, Shanxi 030051, P. R. China

Comptes Rendus. Mathématique, Volume 359 (2021) no. 6, pp. 645-650.

Abstract

We give a simple proof of a result on the $\partial \bar{\partial}$ -lemma property under a blow-up transformation by Deligne–Griffiths–Morgan–Sullivan’s criterion. Here, we use an explicit blow-up formula for Dolbeault cohomology given in our previous work, which can be induced by a morphism expressed on the level of spaces of forms and currents. At last, we discuss the heredity and bimeromorphic invariance of the $\partial \bar{\partial}$ -lemma property.

Received: 2020-12-07
Revised: 2021-03-31
Accepted: 2021-03-31
Published online: 2021-08-25

DOI: 10.5802/crmath.203

Classification: 32Q99

Author's affiliations:

Lingxu Meng ¹

¹ Department of Mathematics, North University of China, Taiyuan, Shanxi 030051, P. R. China

License:

CC-BY 4.0

Copyrights: The authors retain unrestricted copyrights and publishing rights

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     author = {Lingxu Meng},
     title = {The heredity and bimeromorphic invariance of the $\partial \protect \,\protect \overline{\protect \!\partial }$-lemma property},
     journal = {Comptes Rendus. Math\'ematique},
     pages = {645--650},
     publisher = {Acad\'emie des sciences, Paris},
     volume = {359},
     number = {6},
     year = {2021},
     doi = {10.5802/crmath.203},
     language = {en},
}

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Lingxu Meng. The heredity and bimeromorphic invariance of the $\partial \protect \,\protect \overline{\protect \!\partial }$-lemma property. Comptes Rendus. Mathématique, Volume 359 (2021) no. 6, pp. 645-650. doi : 10.5802/crmath.203. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.5802/crmath.203/

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