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arXiv · 2610.16962

Crepant resolutions of four-dimensional finite quotients

Dominik Burek·Sławomir Cynk
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Abstract

We give counterexamples to the conjecture of Dais-Henk-Ziegler on projective crepant resolutions of complete-intersection quotient singularities. For finite $G\subset\operatorname{SL}_4(\mathbb{Z})$, we determine whether $\mathbb{C}^4/G$ admits a projective crepant resolution, with the representations considered up to conjugacy in $\operatorname{SL}_4(\mathbb{C})$. Ten explicit criteria decide all cases. The examples also show that the Molien series and the age polynomial do not determine existence. We also discuss questions of Ito-Reid on maximal cyclic subgroups and the generation of cohomology in degree two.

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Dominik Burek, Sławomir Cynk. 2026-10-12. Crepant resolutions of four-dimensional finite quotients. https://arxiv.org/abs/2610.16962

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