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PreprintCC BY 4.0arXiv

Normal complex surface singularities with rational homology disk smoothings

  • Márton Beke
  • Heesang Park
  • Dongsoo Shin
  • András I. Stipsicz
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Abstract

We prove that a normal surface singularity whose minimal good resolution graph has at least two nodes does not admit a rational homology disk smoothing. Together with the earlier graph classifications and the analytic classifications of Fowler and Wahl, this gives a complete classification of normal surface singularities admitting rational homology disk smoothings and proves Wahl's conjecture. The same argument also proves Wahl's Rational Conjecture.

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Cite

BibTeXRIS
BibTeX
@misc{beke2026normal,
  title = {{Normal complex surface singularities with rational homology disk smoothings}},
  author = {Márton Beke and Heesang Park and Dongsoo Shin and András I. Stipsicz},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.20991},
  eprint = {2610.20991},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.20991},
  note = {CC BY 4.0},
}
RIS
TY  - UNPB
TI  - Normal complex surface singularities with rational homology disk smoothings
AU  - Márton Beke
AU  - Heesang Park
AU  - Dongsoo Shin
AU  - András I. Stipsicz
PY  - 2026
DA  - 2026/10/14
PB  - arXiv
DO  - 10.48550/arxiv.2610.20991
UR  - https://arxiv.org/abs/2610.20991
AB  - We prove that a normal surface singularity whose minimal good resolution graph has at least two nodes does not admit a rational homology disk smoothing. Together with the earlier graph classifications and the analytic classifications of Fowler and Wahl, this gives a complete classification of normal surface singularities admitting rational homology disk smoothings and proves Wahl's conjecture. The same argument also proves Wahl's Rational Conjecture.
ER  -