Nef Cones of the Hilbert Schemes of Points on Generalized Cayley K3 Surfaces

We study the nef cones and fundamental domains of Hilbert schemes of points on the Cayley K3 surface $S$ and its generalizations $S_a$. For the Hilbert square $S^{[2]}$, we explicitly compute the nef cone and describe a fundamental domain using the automorphisms of $S^{[2]}$ and lattice-theoretic methods. For higher Hilbert schemes $S_a^{[n]}$, we determine the nef cones using Bridgeland stability methods that identify the contracted curves defining walls and the divisors generating the extremal rays.