5 papers
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…
A Criteria of Weighted Homogeneity via Logarithmic Vector Fields
Jihao Liu, Xiping Zhang
Recently in [6] the authors proposed a conjecture that the homogeneity of an isolated hypersurface germ can be detected by the existence of non-degenerate holomorphic logarithmic v…
Microlocal indices and Chern Classes of Foliations
Xia Liao, Xiping Zhang
In this paper, we study how global index formulas arise in the theory of one-dimensional holomorphic foliation from the microlocal point of view. We give short proofs and generaliz…
A Syzygy Rank Characterization of Strongly Euler Homogeneity for Projective Hypersurfaces
Xia Liao, Xiping Zhang
In this paper we give a characterization of strongly Euler homogeneous singular points on a reduced complex projective hypersurface $D=V(f)\subset \PP^n$ using the Jacobian syzygie…
Logrithmic Versions of Ginzburg's Sharp Operation for Free Divisors
Xia Liao, Xiping Zhang
Let be a complex manifold, a free divisor and its complement. In this paper we study the characteristic cycle $\textup{CC}(γ\cdot \ind_U)$ of the…