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

Chiwon Yoon

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arXiv · 2602.04499

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

Chiwon Yoon

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Abstract

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.

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Chiwon Yoon. 2026-02-04. Nef Cones of the Hilbert Schemes of Points on Generalized Cayley K3 Surfaces. https://arxiv.org/abs/2602.04499

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