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I'm starting to study K3 surfaces and i have seen many examples of them as Kummer surfaces, smooth quartic in $\mathbb{P}^3$, double covering of $\mathbb{P}^2$ ramified over a smooth sextic...

But no book i have read (i'm referring principally to huybrechts' notes) seems to deal the examples of hodge isometries between K3 surfaces.

Do you have or do you know where i could find some enlightening examples?

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  • $\begingroup$ Are you looking for Hodge isometries between the $H^2$ or just between the transcendental lattices? (If the former, any Hodge isometry can be converted to an isomorphism of K3 after composing by a Weyl group element.) $\endgroup$
    – Abhinav Kumar
    Commented Jun 4, 2013 at 17:43
  • $\begingroup$ no actually i'm looking for isometries between the $H^2$. Also i'd prefer to find them not induced from isomorphisms between the surfaces $\endgroup$
    – dean
    Commented Jun 4, 2013 at 17:48
  • $\begingroup$ you might want to have a look at Morrison's 1987 paper "Isogenies between Algebraic Surfaces with Geometric Genus One". $\endgroup$
    – Christian Liedtke
    Commented Jun 8, 2013 at 12:08

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