Frobenius Structures and Generalized Deformation of Kodaira Manifolds

TL;DR

This paper investigates the Frobenius structures arising from generalized deformations on Kodaira manifolds, showing that on primary Kodaira manifolds, these structures are trivial, extending previous results on Kodaira surfaces.

Contribution

It demonstrates that the Frobenius structure on the degree-2 component of the extended moduli space is trivial for primary Kodaira manifolds, generalizing earlier findings.

Findings

Frobenius structures are trivial on primary Kodaira manifolds

Generalizes previous results on Kodaira surfaces

Connects extended deformation with geometric structures

Abstract

It is known that generalized deformation in the sense of Hitchin-Gaultieri is a geometric realization of the degree-2 component of Kontsevich-Barannikov's homological approach to extended deformation. Through extended deformation, one associates a Frobenius structure to the extended moduli space. In this notes, we prove that on primary Kodaira manifolds the restriction of the Frobenius structure on the degree-2 component of the extended moduli space is trivial. It generalizes the author's past observation on Kodaira surface.