A period map for generalized deformations

TL;DR

This paper extends Griffith's period map to generalized deformations of compact Kaehler manifolds using advanced algebraic structures, providing a new perspective on deformation theory.

Contribution

It introduces a canonical extension of the period map to generalized deformations via Maurer-Cartan solutions in polyvector fields, utilizing Cartan homotopy and L-infinity structures.

Findings

Constructs a canonical extension of the period map

Uses Cartan homotopy and L-infinity algebra on mapping cones

Provides a new framework for generalized deformation theory

Abstract

For every compact Kaehler manifold we give a canonical extension of Griffith's period map to generalized deformations, intended as solutions of Maurer-Cartan equation in the algebra of polyvector fields. Our construction involves the notion of Cartan homotopy and a canonical L-infinity structure on mapping cones of morphisms of differential graded Lie algebras.