Huaiqing Zuo
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View article: Polar loci of multivariable archimedean zeta functions
Polar loci of multivariable archimedean zeta functions Open
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 support locus of F, a topological invariant. We give a relat…
View article: On Stringy E-functions and the Non-negativity Conjecture for Determinantal Varieties
On Stringy E-functions and the Non-negativity Conjecture for Determinantal Varieties Open
We compute the stringy E-functions of determinantal varieties and establish that the stringy E-function of a determinantal variety coincides with the E-function of the product of a Grassmannian and an affine space. Furthermore, a similar r…
View article: The Nakai Conjecture for isolated hypersurface singularities of modality $\le 2$
The Nakai Conjecture for isolated hypersurface singularities of modality $\le 2$ Open
The well-known Nakai Conjecture concerns a very natural question: For an algebra of finite type over a characteristic zero field, if the ring of its differential operators is generated by the first order derivations, is the algebra regular…
View article: Classification of unimodal isolated complete intersection singularities in positive characteristic
Classification of unimodal isolated complete intersection singularities in positive characteristic Open
In this paper we classify the unimodal isolated complete intersection singularities in arbitrary characteristic under contact equivalence. The classification over $\mathbb{C}$ has already done by A. Dimca and C.G. Gibson. We continue and g…
View article: On jet closures of singularities
On jet closures of singularities Open
Jet closure and jet support closure were first introduced by de Fernex, Ein and Ishii to solve the local isomorphism problem. In this paper we introduce two local algebras associated to jet closure and jet support closure, respectively. We…
View article: On Motivic Zeta Functions and Stringy E-function via Embedded $\mathbb{Q}$-Resolution
On Motivic Zeta Functions and Stringy E-function via Embedded $\mathbb{Q}$-Resolution Open
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 for stringy E-function using embedded $\mathbb{Q}$-resolut…
View article: Motivic principal value integrals for hyperplane arrangements
Motivic principal value integrals for hyperplane arrangements Open
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 stronger positive answer to this conjecture for hyperplane arra…
View article: Variation of Archimedean Zeta Function and $n/d$-Conjecture for Generic Multiplicities
Variation of Archimedean Zeta Function and $n/d$-Conjecture for Generic Multiplicities Open
For $f_1,...,f_r\in \mathbb C[z_1,...,z_n]\setminus \mathbb C$, we introduce the variation of archimedean zeta function. As an application, we show that the $n/d$-conjecture, proposed by Budur, Mustaţă, and Teitler, holds for generic multi…
View article: Bernstein-Sato functional equations for ideals in positive characteristic
Bernstein-Sato functional equations for ideals in positive characteristic Open
For an ideal of a regular $\cc$-algebra, its Bernstein-Sato polynomial is the monic polynomial of the lowest degree satisfying an Bernstein-Sato functional equation. We generalize the notion of Bernstein-Sato functional equations to the ca…
View article: A characterization and solvability of quasihomogeneous singularities
A characterization and solvability of quasihomogeneous singularities Open
Let (V, 0) be an isolated hypersurface singularity defined by the holomorphic function f :-ރalgebra and it depends only on the isomorphism class of the germ (V, 0).It is a natural question to ask for a necessary and sufficient condition …
View article: On the Tensor Property of Bernstein-Sato Polynomial
On the Tensor Property of Bernstein-Sato Polynomial Open
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 two effective divisors on the product of two arbitrary non-s…
View article: Classification of weighted dual graphs consisting of $-2$-curves and exactly one $-3$-curve
Classification of weighted dual graphs consisting of $-2$-curves and exactly one $-3$-curve Open
Let $(V, p)$ be a normal surface singularity. Let $\pi\colon (M, A)\to (V, p)$ be a minimal good resolution of $V$. The weighted dual graphs $\Gamma$ associated with $A$ completely describes the topology and differentiable structure of the…
View article: On the Dimension of a New Class of Derivation Lie Algebras Associated to Singularities
On the Dimension of a New Class of Derivation Lie Algebras Associated to Singularities Open
Let (V,0)={(z1,…,zn)∈Cn:f(z1,…,zn)=0} be an isolated hypersurface singularity with mult(f)=m. Let Jk(f) be the ideal generated by all k-th order partial derivatives of f. For 1≤k≤m−1, the new object Lk(V) is defined to be the Lie algebra o…
View article: ON THE DERIVATION LIE ALGEBRAS OF FEWNOMIAL SINGULARITIES
ON THE DERIVATION LIE ALGEBRAS OF FEWNOMIAL SINGULARITIES Open
Let $V$ be a hypersurface with an isolated singularity at the origin defined by the holomorphic function $f:(\mathbb{C}^{n},0)\rightarrow (\mathbb{C},0)$ . The Yau algebra, $L(V)$ , is the Lie algebra of derivations of the moduli algebra o…
View article: 4d N=2 SCFT and singularity theory Part III: Rigid singularity
4d N=2 SCFT and singularity theory Part III: Rigid singularity Open
We classify three fold isolated quotient Gorenstein singularity $C^3/G$. These singularities are rigid, i.e. there is no non-trivial deformation, and we conjecture that they define 4d $\mathcal{N}=2$ SCFTs which do not have a Coulomb branc…
View article: 4d N=2 SCFT and singularity theory Part II: Complete intersection
4d N=2 SCFT and singularity theory Part II: Complete intersection Open
We classify three dimensional isolated weighted homogeneous rational complete intersection singularities, which define many new four dimensional N=2 superconformal field theories. We also determine the mini-versal deformation of these sing…