For K3^[n]-type hyper-Kähler manifolds with antisymplectic involution from ample class of square 2 and divisibility 2, one fixed component is Fano of index 3; the second component in the LLSvS 8-fold is of general type.
Algebra 438 (2015), 90--118
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The geometry of antisymplectic involutions, II
For K3^[n]-type hyper-Kähler manifolds with antisymplectic involution from ample class of square 2 and divisibility 2, one fixed component is Fano of index 3; the second component in the LLSvS 8-fold is of general type.