Stringy Chow rings and weighted blow ups

TL;DR

This paper computes the stringy Chow ring for certain algebraic stacks and weighted blow ups, analyzing their algebraic structure and finite generation properties over various fields.

Contribution

It introduces methods to compute the stringy Chow ring for stacks [X/G] and weighted blow ups, extending previous work to non-algebraically closed fields.

Findings

Computed the stringy Chow ring for [X/G] stacks.

Analyzed the structure of the ring for weighted blow ups.

Explored finite generation properties of the ring.

Abstract

We compute the stringy chow ring of a general Deligne-Mumford stack of the form [X/G] for a smooth variety X and diagonalizable group scheme G, working over a base field that is not necessarily algebraically closed. We then specialize to the stringy chow ring of the weighted blow up of a smooth variety along a smooth center. We explore finite generation properties of this ring.