The formal Kuranishi parametrization via the universal homological perturbation theory solution of the deformation equation

TL;DR

This paper develops a formal framework for miniversal deformations in deformation theory using homological perturbation theory, extending the Kuranishi method to complex manifolds.

Contribution

It introduces a formal version of the Kuranishi parametrization via universal homological perturbation theory for deformation problems.

Findings

Provides a formal solution to the deformation equation

Extends Kuranishi method to a broader algebraic setting

Offers a new approach for analyzing complex manifold deformations

Abstract

Using homological perturbation theory, we develop a formal version of the miniversal deformation associated with a deformation problem controlled by a differential graded Lie algebra over a field of characteristic zero. Our approach includes a formal version of the Kuranishi method in the theory of deformations of complex manifolds.