Nakai conjectures for isolated homogeneous hypersurface singularities
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arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2026
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| _version_ | 1866913065552838656 |
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| author | Yau, Stephen S. -T. Zhu, Qiwei Zuo, Huaiqing |
| author_facet | Yau, Stephen S. -T. Zhu, Qiwei Zuo, Huaiqing |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2604_24508 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Nakai conjectures for isolated homogeneous hypersurface singularities Yau, Stephen S. -T. Zhu, Qiwei Zuo, Huaiqing Algebraic Geometry 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. |
| title | Nakai conjectures for isolated homogeneous hypersurface singularities |
| topic | Algebraic Geometry |
| url | https://arxiv.org/abs/2604.24508 |