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Comptes Rendus. Mathématique
Analyse et géométrie complexes
The heredity and bimeromorphic invariance of the ¯-lemma property
Comptes Rendus. Mathématique, Tome 359 (2021) no. 6, pp. 645-650.

We give a simple proof of a result on the ¯-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 ¯-lemma property.

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DOI : https://doi.org/10.5802/crmath.203
Classification : 32Q99
Lingxu Meng 1

1. Department of Mathematics, North University of China, Taiyuan, Shanxi 030051, P. R. China
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     title = {The heredity and bimeromorphic invariance of the $\partial \protect \,\protect \overline{\protect \!\partial }$-lemma property},
     journal = {Comptes Rendus. Math\'ematique},
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     year = {2021},
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Lingxu Meng. The heredity and bimeromorphic invariance of the $\partial \protect \,\protect \overline{\protect \!\partial }$-lemma property. Comptes Rendus. Mathématique, Tome 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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