The integral Chow ring of weighted blow-ups

TL;DR

This paper provides a comprehensive formula for the integral Chow rings of weighted blow-ups, including related computations for weighted projective stacks and Chern classes, advancing algebraic geometry techniques.

Contribution

It introduces a new formula for the integral Chow rings of weighted blow-ups and extends existing methods to weighted projective stacks and Chern class calculations.

Findings

Derived a formula for the integral Chow ring of weighted blow-ups.

Computed the integral Chow rings of weighted projective stack bundles.

Calculated the Chern class of a weighted blow-up.

Abstract

We give a formula for the integral Chow rings of weighted blow-ups. Along the way, we also compute the integral 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.