On local stabilities of $p$-Kähler structures

Abstract

By use of a natural extension map and a power series method, we obtain a local stability theorem for p-Kähler structures with the $(p,p+1)$-th mild $\partial\bar\partial$-lemma under small differentiable deformations.

Several typos have been fixed. Final version to appear in Compositio Mathematica. arXiv admin note: text overlap with arXiv:1609.05637