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Hi, i've just studied the weak global Torelli theorem for K3, which states that, given two K3 surfaces $X$ and $Y$, they are isomorphic if and only there is an Hodge isometry between $H^2(X,\mathbb{Z})$ and $H^2(Y,\mathbb{Z})$.

I didn't find any example of application of this theorem, so i was wondering if you could point out some examples of K3 surfaces which are proven to be isomorphic by the existence of a Hodge isometry

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  • $\begingroup$ The first application is perhaps to the construction of a moduli space for isomorphism classes, based on such Hodge structures. $\endgroup$
    – roy smith
    Commented May 2, 2013 at 0:50

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