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

János Kollçr, András Némethi, Tommaso De Fernex

Research output: Contribution to journalArticlepeer-review

4 Scopus citations

Abstract

In 1978 Durfee conjectured various inequalities between the signature σ and the geometric genus pg 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 of the resolution is unimodular. We also prove the conjectured 'weak' in- equality for all hypersurface singularities and for sufficiently large multiplicity strict complete intersec- tions. The proofs establish general inequalities valid for any numerically Gorenstein normal surface singularity.

Original languageEnglish (US)
Pages (from-to)787-798
Number of pages12
JournalAnnales Scientifiques de l'Ecole Normale Superieure
Volume50
Issue number3
DOIs
StatePublished - May 1 2017

All Science Journal Classification (ASJC) codes

  • General Mathematics

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