The symplectic Deligne-Mumford stack associated to a stacky polytope

TL;DR

This paper introduces a symplectic version of stacky fans by defining stacky polytopes and constructing associated symplectic Deligne-Mumford stacks, establishing their equivalence with stacky fans.

Contribution

It defines stacky polytopes and constructs symplectic Deligne-Mumford stacks, linking them to stacky fans for the first time.

Findings

Defined a new concept of stacky polytope

Constructed symplectic Deligne-Mumford stacks from stacky polytopes

Proved the equivalence between stacks from stacky polytopes and stacky fans

Abstract

We discuss a symplectic counterpart of the theory of stacky fans. First, we define a stacky polytope and construct the symplectic Deligne-Mumford stack associated to the stacky polytope. Then we establish a relation between stacky polytopes and stacky fans: the stack associated to a stacky polytope is equivalent to the stack associated to a stacky fan if the stacky fan corresponds to the stacky polytope.