Nakai conjectures for isolated homogeneous hypersurface singularities
Algebraic Geometry
2026-04-28 v1
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 homogeneous hypersurface singularities.
Cite
@article{arxiv.2604.24508,
title = {Nakai conjectures for isolated homogeneous hypersurface singularities},
author = {Stephen S. -T. Yau and Qiwei Zhu and Huaiqing Zuo},
journal= {arXiv preprint arXiv:2604.24508},
year = {2026}
}
Comments
This paper was submitted to a journal on January 8, 2024