A period map for generalized deformations

Abstract

For every compact Kähler 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 $L_{\infty }$-structure on mapping cones of morphisms of differential graded Lie algebras.