For a primitive polarization h on a K3 surface S, the Tate-Shafarevich group X(S,h) parametrizes exactly the Pic^0(C_η)-torsors admitting a good hyperkähler model.
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The Tate-Shafarevich group of a polarised K3 surface
For a primitive polarization h on a K3 surface S, the Tate-Shafarevich group X(S,h) parametrizes exactly the Pic^0(C_η)-torsors admitting a good hyperkähler model.