Journal of Symplectic Geometry

Volume 13 (2015)

Number 2

Symplectic packings in dimension $4$ and singular curves

Pages: 305 – 342



Emmanuel Opshtein (Institut de Recherche Mathématique Avancée, Université de Strasbourg et CNRS, Strasbourg, France)


The main goal of this paper is to give constructive proofs of several existence results for symplectic embeddings. The strong relation between symplectic packings and singular symplectic curves, which can be derived from McDuff’s inflations on the blow-ups, is revisited through a new inflation technique that lives at the level of the manifold. As an application, we explain constructions of maximal symplectic packings of $\mathbb{P}^2$ by 6, 7 or 8 balls.

Published 13 April 2015