14 papers
The Quotient of Milnor Number by Tjurina Number of Hypersurface Singularities in Arbitrary Characteristic
Hongrui Ma, Huaiqing Zuo
In this paper, we use Hilbert-Samuel multiplicity, Hilbert-Kunz multiplicity, and s-multiplicity to establish a sharp upper bound for the quotient of the generalized Milnor numbers…
Motivic principal value integrals for hyperplane arrangements
Nero Budur, Quan Shi, Huaiqing Zuo
A conjecture of Denef-Jacobs-Veys relates motivic principal value integrals of multivalued rational top-forms with cohomology support loci of rank one local systems. We give a stro…
Spectrum, Tjurina spectrum, and Hertling conjecture for singularities of modality
Quan Shi, Yang Wang, Huaiqing Zuo
Spectrum is an important numerical invariant of an isolated hypersurface singularity, connecting its topological and analytic structures. The well-known Hertling conjecture tells t…
A remarkable subset of poles of the motivic zeta function
Nero Budur, Eduardo de Lorenzo Poza, Quan Shi +1
For any polynomial f with complex coefficients we find a remarkable subset of poles of the motivic zeta function. It is combinatorially determined by any log resolution and it admi…
On the Poles of Real Archimedean Zeta Functions
Zhikuang Chen, Huaiqing Zuo
This paper studies the poles of the real Archimedean zeta function for a weighted homogeneous polynomial with an isolated singularity at the origin. By app…
On the monodromy conjecture, holomorphy conjecture, and embedded Nash problem for Pfaffian ideals
Yifan Chen, Quan Shi, Yongxin Xu +1
We resolve the monodromy conjecture, holomorphy conjecture, and embedded Nash problem for Pfaffian ideals.