8 papers
Derivations of Generalized Moduli Algebras of Isolated Hypersurface Singularities
Zhiwen Liu, Stephen S. -T. Yau
Let be an isolated complex hypersurface singularity defined by . Let be the moduli(Tjurina) algebra, let be the generalize…
Anderson generating function of rank-one Drinfeld Module over rational function fields
Chuangqiang Hu, Xiao-Min Huang, Stephen S. -T. Yau
We establish a fundamental breakthrough in rank-one Drinfeld module arithmetic by deriving explicit formulas over the integral domain $\A = H^{0}(\mathbb{P}^1-P_Ï, \mathcal{O}_{\m…
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…
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…
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…
Regularity estimate and sparse approximation of pathwise robust Duncan-Mortensen-Zakai equation
Yuhua Meng, Zhongjian Wang, Stephen S. T. Yau +1
In this paper, we establish an \textit{a priori} estimate for arbitrary-order derivatives of the solution to the pathwise robust Duncan-Mortensen-Zakai (DMZ) equation within the fr…