Infinitesimal variations of Hodge structure

This lecture deals with the theory of Hodge structures of smooth projective varieties from the " variational " point of view, introduced and developed by Griffiths in the 1980s. Hodge structures of complex smooth projective varieties include information of a transcendental nature (Betti cohomology with integer coefficients), but the variational point of view retains only data of an algebraic nature (Hodge fibers and Gauss-Manin connection). These data are extremely rich and provide information on algebraic cycles, as well as (more surprisingly) global results such as certain generic Torelli theorems, which will be established here in the case of hypersurfaces with trivial canonical fibers of sufficiently high dimension.