The Apollonian circle packing and ample cones for K3 surfaces

TL;DR

This paper demonstrates that the Apollonian circle packing can accurately represent the ample cone of certain K3 surfaces, providing a visual and geometric understanding of their structure.

Contribution

It proves that the Apollonian packing itself can serve as a geometric model for the ample cone of specific K3 surfaces, confirming a conjecture from earlier work.

Findings

Apollonian packing represents the ample cone for certain K3 surfaces

Provides a geometric visualization of the ample cone

Confirms the conjecture linking Apollonian packing to K3 surface ample cones

Abstract

In an earlier work, we gave an Apollonian-like pictorial representation for the ample cone for a class of K3 surfaces. This raises a natural question: Does the Apollonian packing itself represent the ample cone for a K3 surface? In this note, we answer this question in the affirmative.