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arXiv · 1311.1929

Normal complex surface singularities with rational homology disk smoothings

Heesang Park·Dongsoo Shin·András I. Stipsicz
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Abstract

In this paper we show that if the minimal good resolution graph of a normal surface singularity contains at least two nodes (i.e. vertex with valency at least 3) then the singularity does not admit a smoothing with Milnor fiber having rational homology equal to the rational homology of the 4-disk $D^4$ (called a rational homology disk smoothing). Combining with earlier results, this theorem then provides a complete classification of resolution graphs of normal surface singularities with a rational homology disk smoothing, verifying a conjecture of J. Wahl regarding such singularities. Indeed, together with a recent result of J. Fowler we get the complete list of normal surface singularities which admit rational homology disk smoothings.

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Heesang Park, Dongsoo Shin, András I. Stipsicz. 2014-05-07. Normal complex surface singularities with rational homology disk smoothings. https://arxiv.org/abs/1311.1929

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