K-theory of Weighted Blowups

Veronica Arena; Alessio Cela; Alberto Landi; Michele Pernice

K-theory of Weighted Blowups

Algebraic Geometry 2026-07-24 v1 K-Theory and Homology

Authors: Veronica Arena , Alessio Cela , Alberto Landi , Michele Pernice

Abstract

We compute the K-theory of weighted blowups of smooth stacks satisfying the resolution property along smooth centers. As an application, we determine the K-theory of the stack of stable genus 1 curves with 2 marked points. Furthermore, we express the Lambda polynomial of the tangent complex of the blowup morphism in terms of the blowup data. Along the way, we extend the operational K-theory from torus actions to actions of smooth affine algebraic groups.

Keywords

K-theory weighted blowups algebraic stacks moduli of curves Lambda polynomial operational K-theory

Cite

@article{arxiv.2607.22918,
  title  = {K-theory of Weighted Blowups},
  author = {Veronica Arena and Alessio Cela and Alberto Landi and Michele Pernice},
  journal= {arXiv preprint arXiv:2607.22918},
  year   = {2026}
}

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