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arXiv · 1411.1039

Durfee's conjecture on the signature of smoothings of surface singularities

Tommaso de Fernex·János Kollár·András Némethi
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Abstract

In 1978 Durfee conjectured various inequalities between the signature and the geometric genus of a normal surface singularity. Since then a few counter examples have been found and positive results established in some special cases. We prove a `strong' Durfee--type inequality for any smoothing of a Gorenstein singularity, provided that the intersection form the resolution is unimodular, and the conjectured `weak' inequality for all hypersurface singularities and for sufficiently large multiplicity strict complete intersections. The proofs establish general inequalities valid for any normal surface singularity.

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Tommaso de Fernex, János Kollár, András Némethi. 2014-11-04. Durfee's conjecture on the signature of smoothings of surface singularities. https://arxiv.org/abs/1411.1039

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