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PreprintCC0arXiv

Non-existence of Negative Weight Derivations of the Moduli Algebras of Isolated Weighted Homogeneous Hypersurface Singularities

  • Guorui Ma
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Abstract

Mather and Yau proved that the analytic isomorphism class of an isolated complex hypersurface singularity is determined by its dimension and its moduli algebra. Yau's conjecture asserts that the moduli algebra of an isolated weighted homogeneous hypersurface singularity over ℂ has no nonzero derivation of negative degree. We prove this conjecture. The proof uses Varchenko\textquotesingle s theorem on the μ-constant stratum of an isolated weighted homogeneous singularity, also stated by M. Saito.

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Cite

BibTeXRIS
BibTeX
@misc{ma2026nonexistence,
  title = {{Non-existence of Negative Weight Derivations of the Moduli Algebras of Isolated Weighted Homogeneous Hypersurface Singularities}},
  author = {Guorui Ma},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.25177},
  eprint = {2610.25177},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.25177},
  note = {CC0},
}
RIS
TY  - UNPB
TI  - Non-existence of Negative Weight Derivations of the Moduli Algebras of Isolated Weighted Homogeneous Hypersurface Singularities
AU  - Guorui Ma
PY  - 2026
DA  - 2026/10/18
PB  - arXiv
DO  - 10.48550/arxiv.2610.25177
UR  - https://arxiv.org/abs/2610.25177
AB  - Mather and Yau proved that the analytic isomorphism class of an isolated complex hypersurface singularity is determined by its dimension and its moduli algebra. Yau's conjecture asserts that the moduli algebra of an isolated weighted homogeneous hypersurface singularity over ℂ has no nonzero derivation of negative degree. We prove this conjecture. The proof uses Varchenko\textquotesingle s theorem on the μ-constant stratum of an isolated weighted homogeneous singularity, also stated by M. Saito.
ER  -