Proper good quotients for $\mathbf{G}_m$-actions

Xucheng Zhang

Proper good quotients for $\mathbf{G}_m$-actions

Algebraic Geometry 2024-06-17 v1

Authors: Xucheng Zhang

Abstract

We give an algebraic proof of a result, due to Bialynicki-Birula and Sommese, characterizing the invariant open subsets of a normal proper variety equipped with a $\mathbf{G}_m$ -action that admit a proper good quotient. A major ingredient is the existence result for moduli spaces of algebraic stacks due to Alper, Halpern-Leistner and Heinloth.

Keywords

algebraic group actions

Cite

@article{arxiv.2406.09912,
  title  = {Proper good quotients for $\mathbf{G}_m$-actions},
  author = {Xucheng Zhang},
  journal= {arXiv preprint arXiv:2406.09912},
  year   = {2024}
}

Comments

30 pages, 3 figures

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