Ample vector bundles and moduli of tame stacks
Daniel Bragg, Martin Olsson, and Rachel Webb

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.
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Taxonomy
TopicsAlgebraic Geometry and Number Theory · Advanced Differential Equations and Dynamical Systems · Mathematical Dynamics and Fractals
