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∞-structure on mapping cones of morphisms of differential graded Lie algebras.
Cite this article
Domenico Fiorenza, Marco Manetti, A period map for generalized deformations. J. Noncommut. Geom. 3 (2009), no. 4, pp. 579–597DOI 10.4171/JNCG/47