English

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}
}