2 citations · 4 across the 10 of their papers we have counts for
11 papers
Structure of Torus Fibration Under the First Betti Number Restriction
Xin Peng, Bing Wang, Zhenjian Wang
We study torus bundles with affine structure groups. First, we establish a rigidity result under constraints on the first Betti numbers: If $ \text{b}_{1}(M)-\text{b}_{1}(N)=\dim M…
New proofs for technical results in "Infinitesimal invariants of mixed Hodge structures'' (arXiv:2406.17118v1)
Zhenjian Wang
Cubic forms are constructed in the work of R. Aguilar, M. Green and P. Griffiths to establish the generic global Torelli theorem for Fano-K3 pairs , where is a…
On Strong Lefschetz Property of 0-dimensional Complete Intersections and Associated Forms
Zhenjian Wang
We prove that a homogeneous 0-dimensional complete intersection satisfies the Strong Lefschetz Property (SLP) in degree 1 if and only if its associated form has nonzero Hessian. Th…
Self-intersection Number of Negative Curves on Fermat Surfaces
Zhenjian Wang
We give an explicit formula for the self-intersection number of negative curves on Fermat surfaces. The formula offers us hints to either prove or disprove the Bounded Negativity C…
Deformation of Milnor Algebras
Zhenjian Wang
We investigate deformations of Milnor algebras of smooth homogeneous polynomials, and prove in particular that any smooth degree homogeneous polynomial in variables that…
Monotonic invariants under blowups
Zhenjian Wang
We prove that the numerical invariant of a reduced irreducible plane curve singularity germ is non-negative, non-decreasing under blowups and strictly increasing unless the…
On homogeneous polynomials determined by their partial derivatives
Zhenjian Wang
We prove that a generic homogeneous polynomial of degree is determined, up to a nonzero constant multiplicative factor, by the vector space spanned by its partial derivatives o…
On Deformations of Nodal Hypersurfaces
Zhenjian Wang
We extend the infinitesimal Torelli theorem for smooth hypersurfaces to nodal hypersurfaces.
On algebraic surfaces associated to line arrangements
Zhenjian Wang
For a line arrangement in the complex projective plane , we investigate the compactification of the affine Milnor fiber in and its minim…
On tangential deformations of homogeneous polynomials
Zhenjian Wang
The Jacobian ideal provides the set of infinitesimally trivial deformations for a homogeneous polynomial, or for the corresponding complex projective hypersurface. In this article,…
On homogeneous polynomials determined by their Jacobian ideal
Zhenjian Wang
We investigate which homogeneous polynomials are determined by their Jacobian ideals, and extend and complete previous results due to J. Carlson and Ph. Griffiths, K. Ueda and M. Y…