Categories of symplectic toric manifolds as Picard stack torsors

TL;DR

This paper demonstrates that the stack of symplectic toric G-manifolds over a fixed orbit space functions as a torsor for the stack of symplectic toric G-principal bundles, revealing a deep structural relationship.

Contribution

It provides a proof that the stack of symplectic toric G-manifolds is a torsor for the stack of symplectic toric G-principal bundles over a fixed orbit space.

Findings

Establishes the torsor relationship between symplectic toric G-manifolds and principal bundles.

Clarifies the categorical structure of symplectic toric manifolds.

Provides a foundational result for understanding symplectic toric geometry.

Abstract

We outline a proof that the stack of symplectic toric G-manifolds over a fixed orbit space W is a torsor for the stack of symplectic toric G-principal bundles over W.