Symplectic capacities, unperturbed curves, and convex toric domains

TL;DR

This paper introduces a new sequence of symplectic capacities derived from explicit pseudoholomorphic curve techniques, computes them for convex toric domains, and applies these to obstruct stabilized symplectic embeddings, sometimes achieving sharp results.

Contribution

It defines a new sequence of symplectic capacities using explicit pseudoholomorphic curves and computes them for convex toric domains, providing new sharp obstructions to symplectic embeddings.

Findings

New symplectic capacities for convex toric domains

Sharp obstructions to stabilized symplectic embeddings

Explicit computation without virtual perturbations

Abstract

We use explicit pseudoholomorphic curve techniques (without virtual perturbations) to define a sequence of symplectic capacities analogous to those defined recently by the second named author using symplectic field theory. We then compute these capacities for all four-dimensional convex toric domains. This gives various new obstructions to stabilized symplectic embedding problems which are sometimes sharp.