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For posterity reasons I should mention http://www.math.purdue.edu/~dvb/preprints/book-chap17.pdf which is the best / most readable resource I've seen so far on the subject of Hodge numbers of hypersurfaces. It's probably no coincidence that he also wrote the code on which I based my implementation.

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A HTML5 visualisation of Serre duality and Hodge diamonds

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