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

TL;DR

This paper investigates the nef cones of Hilbert schemes of points on Cayley K3 surfaces and their generalizations, providing explicit computations for the Hilbert square and using Bridgeland stability for higher cases.

Contribution

It explicitly computes the nef cone for the Hilbert square of Cayley K3 surfaces and introduces Bridgeland stability techniques to determine nef cones for higher Hilbert schemes.

Findings

Explicit nef cone for $S^{[2]}$ with automorphism-based description

Nef cones for $S_a^{[n]}$ determined via Bridgeland stability

Identification of extremal rays and walls in nef cone structure

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.