A counterexample to Durfee conjecture

Details A counterexample to Durfee conjecture A counterexample to Durfee conjecture

2011-09-22

arxiv.org/abs/1109.4869v4

Mathematics

Algebraic Geometry

final version, to appear in Comptes Rendus math\'ematiques

Scientific paper

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.

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