A counterexample to a conjecture of Duncan on versal actions

Federico Scavia

A counterexample to a conjecture of Duncan on versal actions

Algebraic Geometry 2026-07-27 v1

Authors: Federico Scavia

Abstract

We disprove a conjecture of Duncan asserting that versality of a faithful finite group action can be detected on Sylow subgroups. Our counterexample is an action of $(C_7\rtimes C_3)\times C_2$ on a degree- $2$ Del Pezzo surface.

Keywords

versal actions Sylow subgroups Del Pezzo surfaces counterexample finite group actions

Cite

@article{arxiv.2607.25118,
  title  = {A counterexample to a conjecture of Duncan on versal actions},
  author = {Federico Scavia},
  journal= {arXiv preprint arXiv:2607.25118},
  year   = {2026}
}

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5 pages