4 papers · 1 filter
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…