Comptes Rendus
Complex analysis/Differential geometry
Extension formulas and deformation invariance of Hodge numbers
Comptes Rendus. Mathématique, Volume 353 (2015) no. 11, pp. 979-984.

We introduce a canonical isomorphism from the space of pure-type complex differential forms on a compact complex manifold to the one on its infinitesimal deformations. By use of this map, we generalize an extension formula in a recent work of K. Liu, X. Yang and the second author. As a direct corollary of the extension formulas, we prove several deformation invariance theorems for Hodge numbers on some certain classes of complex manifolds, without using the Frölicher inequality or the topological invariance of the Betti numbers.

Nous introduisons un isomorphisme canonique entre l'espace des formes différentielles complexes de type pur sur une variété complexe, compacte, et celui de ses déformations infinitésimales, et nous l'utilisons pour généraliser la formule d'extension récemment obtenue par K. Liu, X. Yang et le second auteur. Comme corollaire direct des formules d'extension, nous établissons plusieurs théorèmes d'invariance par déformation des nombres de Hodge des variétés complexes, sans avoir recours à l'inégalité de Frölicher ou à l'invariance topologique des nombres de Betti.

Published online:
DOI: 10.1016/j.crma.2015.09.004
Keywords: Deformations of complex structures, Deformations and infinitesimal methods, Formal methods, Deformations, Hermitian and Kählerian manifolds

Quanting Zhao 1, 2; Sheng Rao 3, 4

1 School of Mathematics and statistics, Central China Normal University, Wuhan 430079, China
2 Center of Mathematical Sciences, Zhejiang University, Hangzhou 310027, China
3 School of Mathematics and statistics, Wuhan University, Wuhan 430072, China
4 Department of Mathematics, University of California at Los Angeles, CA 90095-1555, USA
     author = {Quanting Zhao and Sheng Rao},
     title = {Extension formulas and deformation invariance of {Hodge} numbers},
     journal = {Comptes Rendus. Math\'ematique},
     pages = {979--984},
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     number = {11},
     year = {2015},
     doi = {10.1016/j.crma.2015.09.004},
     language = {en},
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Quanting Zhao; Sheng Rao. Extension formulas and deformation invariance of Hodge numbers. Comptes Rendus. Mathématique, Volume 353 (2015) no. 11, pp. 979-984. doi : 10.1016/j.crma.2015.09.004.

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