A Criteria of Weighted Homogeneity via Logarithmic Vector Fields

Jihao Liu; Xiping Zhang

A Criteria of Weighted Homogeneity via Logarithmic Vector Fields

Algebraic Geometry 2026-06-29 v1

Authors: Jihao Liu , Xiping Zhang

Abstract

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 vector fields. In this paper we prove this conjecture affirmatively.

Keywords

weighted homogeneity hypersurface singularity logarithmic vector fields isolated singularity

Cite

@article{arxiv.2606.29886,
  title  = {A Criteria of Weighted Homogeneity via Logarithmic Vector Fields},
  author = {Jihao Liu and Xiping Zhang},
  journal= {arXiv preprint arXiv:2606.29886},
  year   = {2026}
}