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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.
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Accepted
Original proof of Lefschetz's theorem on $(1,1)$ classes
I like chapter 6 of
Lewis, James D. A survey of the Hodge conjecture,
Second edition, Appendix B by B. Brent Gordon, CRM Monogr. Ser., 10, American Mathematical Society, Providence, RI, 1999.
It has l …