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 language | English (US) |
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Pages (from-to) | 787-798 |
Number of pages | 12 |
Journal | Annales Scientifiques de l'Ecole Normale Superieure |
Volume | 50 |
Issue number | 3 |
DOIs | |
State | Published - May 1 2017 |
All Science Journal Classification (ASJC) codes
- General Mathematics