Ishii's conjecture and Bridgeland stability conditions for dihedral reflection groups

Shu Nimura

Ishii's conjecture and Bridgeland stability conditions for dihedral reflection groups

Algebraic Geometry 2026-05-22 v1

Authors: Shu Nimura

Abstract

We provide a new proof of Ishii's conjecture for any dihedral reflection group $G\subset GL_2(\mathbb{C})$ from the viewpoint of Bridgeland stability conditions. Our strategy is to reduce the problem, via the derived McKay correspondence, to a geometric construction of Bridgeland stability conditions on the root stack of the maximal resolution along the strict transform of the discriminant divisor.

Keywords

Ishii conjecture dihedral reflection groups Bridgeland stability conditions derived McKay correspondence root stack discriminant divisor

Cite

@article{arxiv.2605.22474,
  title  = {Ishii's conjecture and Bridgeland stability conditions for dihedral reflection groups},
  author = {Shu Nimura},
  journal= {arXiv preprint arXiv:2605.22474},
  year   = {2026}
}

Comments

30 pages, 2 figures

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