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arXiv · 1909.12711

Extension formulas and deformation invariance of Hodge numbers

Sheng Rao·Quanting Zhao
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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 Frölicher inequality or the topological invariance of Betti numbers.

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Sheng Rao, Quanting Zhao. 2019-09-27. Extension formulas and deformation invariance of Hodge numbers. https://doi.org/10.1016/j.crma.2015.09.004

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