Trento notes on Hodge theory (Q2898481)

The first half this article is about Hodge theory. It contains the relative version of Hodge theory including the Kodaira-Spencer class and Griffiths transversality as well as the notion of variation of Hodge structure. It discusses Deligne's argument for the degeneration of the Leray spectral sequence of a smooth projective family and introduces mixed Hodge theory. The second half is concerned with period mappings. It begins with Griffiths' description of the Hodge filtration on the primitive cohomology of a smooth hypersurface and then focuses on period mappings which take their values in a locally symmetric variety. It also discusses a number of examples, including \(K3\) surface, quartic curves and cubic hypersurfaces of dimension at most four.