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PreprintCC BY-NC-ND 4.0arXiv

On symplectic aspects of μ-equivalence of a class of isolated hypersurface singularities

  • Chris Peters
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Abstract

A μ-constant deformation of isolated complex hypersurface singularities of dimensions different from 2 preserves the diffeomorphism class of the Milnor fiber. If it would be known that μ-constant deformations have no vanishing folds as defined in by O'Shea, this result is even true in all dimensions since the members in the family would have a common Milnor ball-radius. In this note a symplectic version of this is shown which in particular applies to weighted homogeneous polynomial singularities.

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Cite

BibTeXRIS
BibTeX
@misc{peters2026symplectic,
  title = {{On symplectic aspects of $μ$-equivalence of a class of isolated hypersurface singularities}},
  author = {Chris Peters},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.12589},
  eprint = {2609.12589},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.12589},
  note = {CC BY-NC-ND 4.0},
}
RIS
TY  - UNPB
TI  - On symplectic aspects of μ-equivalence of a class of isolated hypersurface singularities
AU  - Chris Peters
PY  - 2026
DA  - 2026/09/11
PB  - arXiv
DO  - 10.48550/arxiv.2609.12589
UR  - https://arxiv.org/abs/2609.12589
AB  - A μ-constant deformation of isolated complex hypersurface singularities of dimensions different from 2 preserves the diffeomorphism class of the Milnor fiber. If it would be known that μ-constant deformations have no vanishing folds as defined in by O'Shea, this result is even true in all dimensions since the members in the family would have a common Milnor ball-radius. In this note a symplectic version of this is shown which in particular applies to weighted homogeneous polynomial singularities.
ER  -