A counterexample to Durfee conjecture
Algebraic Geometry
2011-11-08 v4 Geometric Topology
Abstract
An old conjecture of Durfee 1978 bounds the ratio of two basic invariants of complex isolated complete intersection surface singularities: the Milnor number and the singularity (or geometric) genus. We give a counterexample for the case of non-hypersurface complete intersections, and we formulate a weaker conjecture valid in arbitrary dimension and codimension. This weaker bound is asymptotically sharp. In this note we support the validity of the new proposed inequality by its verification in certain (homogeneous) cases. In our subsequent paper we will prove it for several other cases and we will provide a more comprehensive discussion.
Cite
@article{arxiv.1109.4869,
title = {A counterexample to Durfee conjecture},
author = {Dmitry Kerner and András Némethi},
journal= {arXiv preprint arXiv:1109.4869},
year = {2011}
}
Comments
final version, to appear in Comptes Rendus math\'ematiques