L-infinity algebras, Cartan homotopies and period maps

Details L-infinity algebras, Cartan homotopies and period maps L-infinity algebras, Cartan homotopies and period maps

2006-05-11

arxiv.org/abs/math/0605297v1

Mathematics

Algebraic Geometry

31 pages, uses xypic

Scientific paper

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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