Global Torelli theorem for K3 surfaces
= Global Torelli theorem for K3 surfaces
{title2=$\phi=f^*:H^2(Y,\mathbb Z)\to H^2(X,\mathbb Z)$}
An integral Hodge isometry between complex <K3 surfaces> which carries some <Kähler class> to a Kähler class is the pullback of a unique <isomorphism> of the surfaces. A Hodge isometry without that cone condition need not itself be geometric: reflection in an effective $(-2)$-curve reverses its class and cannot be induced by an isomorphism.