# The nef cone of the Hilbert scheme of points on rational elliptic surfaces and the cone conjecture

## TL;DR

This paper computes the nef cone of the Hilbert scheme of points on a general rational elliptic surface and verifies the Morrison-Kawamata cone conjecture for these cones.

## Contribution

It provides the first explicit computation of the nef cone for these Hilbert schemes and confirms the cone conjecture in this setting.

## Key findings

- Nef cone of the Hilbert scheme is explicitly determined.
- Morrison-Kawamata cone conjecture holds for these nef cones.
- Supports the conjecture's validity in new geometric contexts.

## Abstract

We compute the nef cone of the Hilbert scheme of points on a general rational elliptic surface. As a consequence of our computation, we show that the Morrison-Kawamata cone conjecture holds for these nef cones.