The integral Chow ring of weighted blow-ups

Arena, Veronica; Obinna, Stephen

doi:10.2140/ant.2025.19.1231

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The integral Chow ring of weighted blow-ups

Veronica Arena and Stephen Obinna

Appendix: Veronica Arena, Stephen Obinna and Dan Abramovich

Vol. 19 (2025), No. 6, 1231–1258

DOI: 10.2140/ant.2025.19.1231

Abstract

We give a formula for the Chow rings of weighted blow-ups. Along the way, we also compute the Chow rings of weighted projective stack bundles, a formula for the Gysin homomorphism of a weighted blow-up, and a generalization of the splitting principle. In addition, in the Appendix we compute the Chern class of a weighted blow-up.

Keywords

weighted projective bundles, weighted affine bundles, Chow groups, intersection theory, weighted blow-ups, algebraic stacks, algebraic geometry, Chow rings, projective stack bundles

Mathematical Subject Classification

Primary: 14E05, 14F43

Milestones

Received: 17 August 2023

Revised: 29 May 2024

Accepted: 16 July 2024

Published: 14 May 2025

Authors

Veronica Arena
Department of Mathematics Brown University Providence, RI United States

Stephen Obinna
Department of Mathematics Brown University Providence, RI United States

Veronica Arena


Stephen Obinna


Dan Abramovich
Department of Mathematics Brown University Providence, RI United States

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Vol. 19, No. 6, 2025