Ample vector bundles and moduli of tame stacks

TL;DR

This paper introduces a method to embed tame stacks into generalized weighted projective stacks using ample vector bundles, enabling the construction of algebraic moduli stacks of tame stacks and orbicurves.

Contribution

It develops a new approach to embed tame stacks via ample vector bundles and constructs associated algebraic moduli stacks, expanding the toolkit for studying tame stacks.

Findings

Embedding tame stacks into weighted projective stacks is possible using ample vector bundles.

Constructed algebraic moduli stacks of tame stacks with ample vector bundles.

Developed a framework for algebraic stacks of tame orbicurves.

Abstract

We explain how to define an embedding of a tame stack over a noetherian ring into a certain generalization of a weighted projective stack using a notion of ample vector bundle on the stack. As applications we construct algebraic moduli stacks of tame stacks equipped with an ample vector bundle and algebraic stacks of tame orbicurves.