Maximal Symplectic packings of $\P^2$

TL;DR

This paper studies the structure of maximal symplectic packings in the complex projective plane, revealing singular points and constructing regular examples with five equal balls, advancing understanding of symplectic packing configurations.

Contribution

It provides a detailed analysis of intersections in maximal packings of 2, identifies singular points, and constructs explicit regular packings with five equal balls.

Findings

Existence of singular points in maximal packings with more than three balls

Construction of regular maximal packings with five equal balls

Analysis of intersection patterns in symplectic packings

Abstract

In this paper we describe the intersection between the balls of maximal symplectic packings of $\P^2$. This analysis shows the existence of singular points for maximal packings of $\P^2$ by more than three equal balls. It also yields a construction of a class of very regular examples of maximal packings by five balls.