Newton-Okoukov bodies and symplectic embeddings into non-toric rational surfaces

TL;DR

This paper introduces new methods using Newton-Okoukov bodies to analyze symplectic embeddings into non-toric rational surfaces, providing sharp results and identifying obstructions.

Contribution

It develops novel techniques for constructing and obstructing symplectic embeddings in non-toric rational surfaces using Newton-Okoukov bodies, expanding understanding beyond toric cases.

Findings

Sharp embedding results for concave toric domains into non-toric surfaces

New obstructions to infinite staircases in non-toric settings

Enhanced methods for symplectic embedding analysis

Abstract

We develop new methods of both constructing and obstructing symplectic embeddings into non-toric rational surfaces using the theory of Newton-Okoukov bodies. Applications include sharp embedding results for concave toric domains into non-toric rational surfaces, and new cases of non-existence for infinite staircases in the non-toric setting.