A period map for generalized deformations

Understand

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.