10 papers
A combinatorial criterion for detecting roots of Bernstein-Sato polynomials
Quan Shi, Huaiqing Zuo
We give a combinatorial criterion for detecting roots of Bernstein-Sato polynomials of ideals. As applications, we prove the strong monodromy conjecture for determinantal and Pfaff…
Zero loci of Bernstein-Sato ideals are not necessarily linear
Quan Shi, Yongxin Xu, Huaiqing Zuo
We find a polynomial map the zero locus of whose Bernstein-Sato ideal is not linear, giving a counterexample to a conjecture of N. Budur.
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 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.
Polar loci of multivariable archimedean zeta functions
Nero Budur, Quan Shi, Huaiqing Zuo
We determine, up to exponentiating, the polar locus of the multivariable archimedean zeta function associated to a finite collection of polynomials F. The result is the monodromy s…
On Motivic Zeta Functions and Stringy E-function via Embedded -Resolution
Yifan Chen, Quan Shi, Huaiqing Zuo
We provide the formula of motivic zeta function for semi-quasihomogeneous singularities and in dimension two, we determine the poles of zeta functions. We also give another formula…
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…
Variation of Archimedean Zeta Function and -Conjecture for Generic Multiplicities
Quan Shi, Huaiqing Zuo
For , we introduce the variation of archimedean zeta function. As an application, we show that the -conjecture, propo…
On the Tensor Property of Bernstein-Sato Polynomial
Quan Shi, Huaiqing Zuo
We prove the multiplicative Thom-Sebastiani rule for Bernstein-Sato polynomials, answering the longstanding questions of Budur and Popa. We generalize the result to the tensor of t…