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L-infinity algebras, Cartan homotopies and period maps

Domenico Fiorenza·Marco Manetti
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Abstract

We prove that, for every compact Kaehler manifold, the period map of its Kuranishi family is induced by a natural L-infinity morphism. This implies, by standard facts about L-infinity algebras, that the period map is a "morphism of deformation theories" and then commutes with all deformation theoretic constructions (e.g. obstructions).

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Domenico Fiorenza, Marco Manetti. 2006-05-11. L-infinity algebras, Cartan homotopies and period maps. https://arxiv.org/abs/math/0605297

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