Let (X,λ)(𝑋,𝜆) be a polarized compact irreducible hyperkahler manifold of K3[n]𝐾3[𝑛]-type. If λ𝜆 has square and divisibility 2, then there is an involution τ∈Aut(X)𝜏∈𝐴𝑢𝑡(𝑋) whose fixed locus has two connected components.

A work of Flapan, Macri, O'Grady and Sacca proves that one of these connected components is a Fano variety. In this talk I will illustrate this result using examples coming from the theory of moduli spaces of stable complexes in a K3 surface.