English

Derived McKay correspondence for real reflection groups of rank three

Algebraic Geometry 2025-04-03 v1

Abstract

We describe the derived McKay correspondence for real reflection groups of rank 33 in terms of a maximal resolution of the logarithmic pair consisting of the quotient variety and the discriminant divisor with coefficient 12\frac{1}{2}. As an application, we verify a conjecture by Polishchuk and Van den Bergh on the existence of a certain semiorthgonal decomposition of the equivariant derived category into the derived categories of affine spaces for any real reflection group of rank 33.

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Cite

@article{arxiv.2504.01387,
  title  = {Derived McKay correspondence for real reflection groups of rank three},
  author = {Akira Ishii and Shu Nimura},
  journal= {arXiv preprint arXiv:2504.01387},
  year   = {2025}
}

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17 pages