The Nakai Conjecture for isolated hypersurface singularities of modality $\le 2$

Rui Li, Zida Xiao, Huaiqing Zuo

Published 2025-02-07Version 1

The well-known Nakai Conjecture concerns a very natural question: For an algebra of finite type over a characteristic zero field, if the ring of its differential operators is generated by the first order derivations, is the algebra regular? And it is natural to extend the Nakai Conjecture to local domains, in this paper, we verify it for isolated hypersurface singularities of modality $\le 2$, this extends the existing works.