Complete intersection hyperk\"{a}hler fourfolds with respect to equivariant vector bundles over rational homogeneous varieties of Picard number one

We classify fourfolds with trivial canonical bundle which are zero loci of general global sections of completely reducible equivariant vector bundles over exceptional homogeneous varieties of Picard number one. As a result, we see that there exist no hyperkähler fourfolds among them. This completes similar classifications by Benedetti and Inoue–Ito–Miura for Grassmannians and isotropic (symplectic or orthogonal) Grassmannians.

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