8 papers · 1 filter
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…