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February 9, 2026International Mathematics Research Notices0 citations

Stringy Chow Rings and Weighted Blow-Ups

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QKQiangru KuangYLYeqin LiuRWRachel Webb

Key Points

  • To compute the stringy Chow ring for a Deligne–Mumford stack and explore its properties in weighted blow-ups.
  • Compute the stringy Chow ring of the form [X/G] for smooth variety X and group scheme G.
  • Specialize findings to weighted blow-ups along a smooth center.
  • Analyze finite generation properties of the stringy Chow ring.
  • Identified the structure of the stringy Chow ring for general Deligne–Mumford stacks.
  • Demonstrated specific scenarios of weighted blow-ups retain desirable properties.
  • Revealed insights into the finite generation of these algebraic objects.

Abstract

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.

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Cite This Study

Kuang et al. (2025) studied this question.

synapsesocial.com/papers/698979e9f0ec2af6756e8041https://doi.org/10.1093/imrn/rnaf374
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