Durfee-type bound for some non-degenerate complete intersection singularities

Dmitry Kerner, András Némethi

Research output: Contribution to journalArticlepeer-review

Abstract

The Milnor number, μ(X, 0) , and the singularity genus, pg(X, 0) , are fundamental invariants of isolated hypersurface singularities (more generally, of local complete intersections). The long standing Durfee conjecture (and its generalization) predicted the inequality μ(X, 0) ≥ (n+ 1) ! pg(X, 0) , here n= dim (X, 0). Recently we have constructed counterexamples, proposed a corrected bound and verified it for the homogeneous complete intersections. In the current paper we treat the case of germs with Newton-non-degenerate principal part when the Newton diagrams are “large enough”, i.e. they are large multiples of some other diagrams. In the case of local complete intersections we prove the corrected inequality, while in the hypersurface case we prove an even stronger inequality.

Original languageEnglish
Pages (from-to)159-175
Number of pages17
JournalMathematische Zeitschrift
Volume285
Issue number1-2
DOIs
StatePublished - 1 Feb 2017

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