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arXiv · 2610.20991

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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Márton Beke, Heesang Park, Dongsoo Shin, András I. Stipsicz. 2026-10-14. Normal complex surface singularities with rational homology disk smoothings. https://arxiv.org/abs/2610.20991

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