[Formules d'extension et invariance par déformation des nombres de Hodge]
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.
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.
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@article{CRMATH_2015__353_11_979_0,
author = {Zhao, Quanting and Rao, Sheng},
title = {Extension formulas and deformation invariance of {Hodge} numbers},
journal = {Comptes Rendus. Math\'ematique},
pages = {979--984},
publisher = {Elsevier},
volume = {353},
number = {11},
year = {2015},
doi = {10.1016/j.crma.2015.09.004},
language = {en},
url = {http://www.numdam.org/articles/10.1016/j.crma.2015.09.004/}
}
TY - JOUR AU - Zhao, Quanting AU - Rao, Sheng TI - Extension formulas and deformation invariance of Hodge numbers JO - Comptes Rendus. Mathématique PY - 2015 SP - 979 EP - 984 VL - 353 IS - 11 PB - Elsevier UR - http://www.numdam.org/articles/10.1016/j.crma.2015.09.004/ DO - 10.1016/j.crma.2015.09.004 LA - en ID - CRMATH_2015__353_11_979_0 ER -
%0 Journal Article %A Zhao, Quanting %A Rao, Sheng %T Extension formulas and deformation invariance of Hodge numbers %J Comptes Rendus. Mathématique %D 2015 %P 979-984 %V 353 %N 11 %I Elsevier %U http://www.numdam.org/articles/10.1016/j.crma.2015.09.004/ %R 10.1016/j.crma.2015.09.004 %G en %F CRMATH_2015__353_11_979_0
Zhao, Quanting; Rao, Sheng. Extension formulas and deformation invariance of Hodge numbers. Comptes Rendus. Mathématique, Tome 353 (2015) no. 11, pp. 979-984. doi : 10.1016/j.crma.2015.09.004. http://www.numdam.org/articles/10.1016/j.crma.2015.09.004/
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