activity
20242026
collaborators

7 papers

math.AG2026

Nakai conjectures for isolated weighted homogeneous hypersurface singularities

Stephen S. -T. Yau, Qiwei Zhu, Huaiqing Zuo

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…

math.AG2026

Tjurina Number Jumps and Unimodal Hypersurface Singularities in Positive Characteristic

Hongrui Ma, Aoyu Ying, Huaiqing Zuo

This paper generalizes existing methods to derive stronger bounds on the modality of hypersurface singularities. Our results demonstrate that each sudden jump in the extended Tjuri…

math.AG2026

Classification of unimodal isolated complete intersection singularities in positive characteristic

Hongrui Ma, Stephen S. -T. Yau, Huaiqing Zuo

In this paper we classify the unimodal isolated complete intersection singularities in arbitrary characteristic under contact equivalence. The classification over has…

math.AG2025

On the -th Tjurina number of weighted homogeneous singularities

Chuangqiang Hu, Stephen S. -T. Yau, Huaiqing Zuo

Let denote an isolated singularity defined by a weighted homogeneous polynomial . Let be the local algebra of holomorphic function germs at the origin…

math.AG2025

The Nakai Conjecture for isolated hypersurface singularities of modality

Rui Li, Zida Xiao, Huaiqing Zuo

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 gener…

math.AG2024

Normal surface singularities of small degrees

Stephen S. -T. Yau, Hao Zuo, Huaiqing Zuo

The notion of the Yau sequence was introduced by Tomaru, as an attempt to extend Yau's elliptic sequence for (weakly) elliptic singularities to normal surface singularities of high…