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I'm reading the paper of Claire Voisin on the Torelli theorem for cubic hypersurfaces of $\mathbb{P}^5$ (in french : Are there lecture notes, or survey articles, or a book on that subject, with full details ? There are a lot of 'clairement' and 'évident'...

In the last section of the paper for example, she proves that the period map, extended to the locus $\Delta$ of cubics with one node (after a degre 2 ramified cover) has maximal rank along $\Delta$. The Clemens-Schmid sequences seems a little different from the one in Peters-Steenbrink and I am not sure about the precise meaning of 'the period map essentially gives this Hodge structure, from what it is obvious that we can reconstruct this other one, etc...'

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In the case you have not yet seen it, there exists an alternative proof by Looijenga. The period map for cubic fourfolds – Dmitri Oct 17 '10 at 20:59

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