For a very general cubic fourfold with two planes meeting along a line, the two associated K3 surfaces are non-isomorphic but are linked by a common double cover that yields a Hodge isometry and a twisted derived equivalence.
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A note on cubic fourfolds containing several planes
For a very general cubic fourfold with two planes meeting along a line, the two associated K3 surfaces are non-isomorphic but are linked by a common double cover that yields a Hodge isometry and a twisted derived equivalence.