Extension formulas and deformation invariance of Hodge numbers
Complex Variables
2019-09-30 v1 Differential Geometry
Abstract
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.
Keywords
Cite
@article{arxiv.1909.12711,
title = {Extension formulas and deformation invariance of Hodge numbers},
author = {Sheng Rao and Quanting Zhao},
journal= {arXiv preprint arXiv:1909.12711},
year = {2019}
}