Formal Kuranishi Families and Period Maps

Abstract

After the results regarding coalgebras and $L_{\infty }$-morphisms proved in Chaps. 11 and 12 we are ready to give some applications of $L_{\infty }$-algebras in deformation theory. The first two sections of this chapter are devoted to the proof that every $L_{\infty }$-morphism induces natural transformations of both Maurer–Cartan and deformation functors, together with an interpretation of the formal Kuranishi family in terms of homotopy transfer of $L_{\infty }$ structure.