The structure of deformed double complexes on the Iwasawa manifold

TL;DR

This paper classifies the deformed double complexes arising from the Kuranishi family of the Iwasawa manifold into three isomorphism types and explicitly describes their structures, also computing their Frölicher spectral sequences.

Contribution

The paper applies Stelzig and Qi-Khovanov's structure theorem to classify and explicitly describe the deformed double complexes in the Kuranishi family of the Iwasawa manifold.

Findings

Exactly 3 isomorphism types of deformed double complexes

Explicit structures of each isomorphism type

Computed Frölicher spectral sequence for each fiber

Abstract

The Kuranishi family of the Iwasawa manifold give rise naturally to a family of (deformed) double complexes. By using the structure theorem of double complexes due to Stelzig and Qi-Khovanov, we show there are exactly $3$ isomorphism types in this family and determine explicitly structures of these $3$ types. As an application, we computed the Fr\"olicher spectral sequence for each fiber in the Kuranishi family of the Iwasawa manifold.