Two-dimensional equivariant symplectic submanifolds in toric manifolds

TL;DR

This paper develops a criterion for identifying two-dimensional equivariant symplectic submanifolds within symplectic toric manifolds by integrating convex geometry and local models.

Contribution

It introduces a new criterion combining Delzant polytope geometry with local symplectic models to classify equivariant symplectic submanifolds.

Findings

Provides a geometric criterion for submanifold classification

Links convex polytope geometry with symplectic submanifold properties

Advances understanding of symplectic submanifold structure in toric manifolds

Abstract

To find all two-dimensional equivariant symplectic submanifolds in symplectic toric manifolds, we combine the convex geometry of Delzant polytopes with local equivariant symplectic models and obtain a criterion for determining when a two-dimensional submanifold is an equivariant symplectic submanifold in a toric manifold.