# Toric Symplectic Stacks

## TL;DR

This paper introduces the concept of toric symplectic stacks, classifies them using convex polytopes with extra data, and demonstrates their deformation to toric orbifolds, extending classical results in symplectic geometry.

## Contribution

It provides an intrinsic definition of toric symplectic stacks and generalizes Delzant's classification to this broader context.

## Key findings

- Toric symplectic stacks are classified by convex polytopes with additional combinatorial data.
- Any toric symplectic stack can be deformed into an ineffective toric orbifold.
- The paper extends classical classification results to a new stacky setting.

## Abstract

We give an intrinsic definition of toric symplectic stacks, and show that they are classified by simple convex polytopes equipped with some additional combinatorial data. This generalizes Delzant's classification of toric symplectic manifolds. As an application, we show that any toric symplectic stack can be deformed to an ineffective toric orbifold.