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arXiv · 2604.24508

Nakai conjectures for isolated weighted homogeneous hypersurface singularities

Stephen S. -T. Yau·Qiwei Zhu·Huaiqing Zuo
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Abstract

The long-standing Nakai Conjecture concerns a very natural question: can differential operators detect singularities on algebraic varieties? On a smooth complex variety, it is well known that the ring of differential operators is generated by derivations. Nakai asked whether the converse holds: if the ring of differential operators is generated by derivations, is the variety smooth? In this paper, we verify the Nakai Conjecture for isolated weighted homogeneous hypersurface singularities.

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Stephen S. -T. Yau, Qiwei Zhu, Huaiqing Zuo. 2026-04-27. Nakai conjectures for isolated weighted homogeneous hypersurface singularities. https://arxiv.org/abs/2604.24508

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