6 papers · 1 filter
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…