The GIT moduli space of codimension four linear sections of the spinor tenfold is isomorphic to the GIT moduli space of Kummer surfaces, explicitly wP(2,3,5,6).
Mukai, Curves, K3 surfaces and Fano 3-folds of genus ≤ 10, Algebraic geometry and commuta- tive algebra, Vol
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On linear sections of the spinor tenfold II
The GIT moduli space of codimension four linear sections of the spinor tenfold is isomorphic to the GIT moduli space of Kummer surfaces, explicitly wP(2,3,5,6).