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The study of harmonic differential forms on complex projective varieties, their invariantly defined filtrations, their integrals over topological cycles, especially over subvarieties, the deformations of these integrals and filtrations in families, and a multitude of generalizations.
2
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Looking for a good exposition - Rees Construction
There are many excellent references. It really depends on what you are after. One of the most comprehensive references is the thesis of Olivier Penacchio: http://arxiv.org/abs/math/0307156.
4
votes
Reference for the Hodge Bundle
The list of references is way too long. Here are some classical texts containing both the setup and calculations:
1) P. Deligne, Le déterminant de la cohomologie, Current Trends in Arithmetical Algeb …
3
votes
Special fiber of the Neron Model of an Abelian scheme in terms of Limit Hodge Structure
Take a look at this classical paper of Clemens. Maybe this is what you are looking for?