Skip to content
DraconiticResearch
Search Sources API
186,625 studies31 sourcesUpdated 4 min ago
PreprintarXiv licencearXiv

Criteria for Weighted Homogeneity via Logarithmic Vector Fields

  • Jihao Liu
  • Xiping Zhang
Open at sourcePDFDOICite

Abstract

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 weighted homogeneity of this hypersurface singularity can be detected by the existence of either a transverse or a non-degenerate holomorphic logarithmic vector fields. In this paper we prove this conjecture affirmatively. We also prove that the GSV index attains the lower bound if and only if the hypersurface singularity is weighted homogeneous.

Related

  1. The classification of taut surface singularities via representations from logarithmic vector fields
    Heesang Park, Dongsoo Shin
    arXivPreprintCC BY 4.0Full textAlgebra & number theoryGeometry & topologyarXiv
  2. Liouville Theorems and Sharp Homogeneity Defects for Weighted Potential Systems
    Shengbing Deng, Bo Zhang
    arXivPreprintarXiv licenceFull textAnalysis & PDEsarXiv
  3. New Criteria for Composition Operators into Weighted Harmonic Bloch Spaces
    Mahmoud Ali Bakhit, Munirah Aljuaid
    AxiomsPeer-reviewedCC BY 4.0General mathematicsCrossref
  4. Vector-Carleson, Calderón, and Poisson-Atomic Criteria for Generalized Hilbert Operators on Hp, p>2
    Yicen Ma
    arXivPreprintarXiv licenceFull textAnalysis & PDEsarXiv
  5. Decay of weighted cusp counts for congruence subgroups of SL2 over number fields
    Shengyuan Zhao
    HALPreprintLicence not statedGeneral mathematicsHAL

Cite

BibTeXRIS
BibTeX
@misc{liu2026criteria,
  title = {{Criteria for Weighted Homogeneity via Logarithmic Vector Fields}},
  author = {Jihao Liu and Xiping Zhang},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2606.29886},
  eprint = {2606.29886},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2606.29886},
}
RIS
TY  - UNPB
TI  - Criteria for Weighted Homogeneity via Logarithmic Vector Fields
AU  - Jihao Liu
AU  - Xiping Zhang
PY  - 2026
DA  - 2026/09/28
PB  - arXiv
DO  - 10.48550/arxiv.2606.29886
UR  - https://arxiv.org/abs/2606.29886
AB  - 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 weighted homogeneity of this hypersurface singularity can be detected by the existence of either a transverse or a non-degenerate holomorphic logarithmic vector fields. In this paper we prove this conjecture affirmatively. We also prove that the GSV index attains the lower bound if and only if the hypersurface singularity is weighted homogeneous.
ER  -