Extension formulas and deformation invariance of Hodge numbers
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 use of Fr\"{o}licher inequality or the topological invariance of Betti numbers.
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Complex Variables
Differential Geometry