6 citations · 10 across the 9 of their papers we have counts for
10 papers
Remarks on the monodromy conjecture for symmetric determinantal hypersurfaces
Renjie Lyu, Xiping Zhang
We compute the local and global Denef--Loeser topological zeta functions of the determinant on the space of symmetric matrices. It verifies the strong monodromy conjecture of the s…
On Free and Nearly Free Conjecture of Rational Unibranched Projective Plane Curves
Xiping Zhang
Let $C\subset \PP^2$ be a reduced irreducible complex plane curve with complement . In this paper we prove that , where is the freeness defect of defin…
Danus: Orchestrating Mathematical Reasoning Agents with Fact-Graph Memory
Jihao Liu, Guoxiong Gao, Zeming Sun +8
Recent LLM-based mathematical reasoning agents have begun to tackle research-level problems and, in several cases, have contributed to the resolution of open problems. However, sca…
Criteria of isolated weighted homogeneous hypersurface singularities using Logarithmic vector fields
Jihao Liu, Xiping Zhang
We prove a conjecture of da Silva Machado and Seade that characterizes weighted homogeneous isolated hypersurface singularities through the existence of a logarithmic vector field…
Criteria for Weighted Homogeneity via Logarithmic Vector Fields
Jihao Liu, Xiping Zhang
Recently in [6] the authors proved a lower bound for the $\GSV$ index of a logarithmic vector field along an isolated hypersurface singularity and proposed a conjecture that the we…
Local Euler Obstructions of Reflective Projective Varieties
Xiping Zhang
In this note we introduce the concept of reflective projective varieties. These are stratified projective varieties with certain dimension constraints on their dual varieties. We p…
Characteristic Classes of Homogeneous Essential Isolated Determinantal Varieties
Xiping Zhang
The (homogeneous) Essentially Isolated Determinantal Variety is the natural generalization of generic determinantal variety, and is fundamental example to study non-isolated singul…
Geometric Invariants of Recursive Group Orbit Stratification
Xiping Zhang
The local Euler obstructions and the Euler characteristics of linear sections with all hyperplanes on a stratified projective variety are key geometric invariants in the study of s…
Local Euler Obstruction and Chern-Mather classes of Determinantal Varieties
Xiping Zhang
For , Let be an algebraic closed base field, and define to be the set of matrices over with kernel dimension . This is a projective…
Chern classes and Characteristic Cycles of Determinantal Varieties
Xiping Zhang
Let be an algebraically closed field of characteristic . For , we define to be the set of matrices over with kernel dimension .…