The 'corrected Durfee's inequality' for homogeneous complete intersections

Dmitry Kerner, András Némethi

Research output: Contribution to journalArticlepeer-review

7 Scopus citations


We address the conjecture of Durfee (Math Ann 232:85-98, 1978), bounding the singularity genus pg by a multiple of the Milnor number μ for an n-dimensional isolated complete intersection singularity. We show that the original conjecture of Durfee, namely (n+1)!· pg ≤ μ, fails whenever the codimension r is greater than one. Moreover, we propose a new inequality Cn,r · pg μ, and we verify it for homogeneous complete intersections. In the homogeneous case the inequality is guided by a 'combinatorial inequality', that might have an independent interest.

Original languageEnglish
Pages (from-to)1385-1400
Number of pages16
JournalMathematische Zeitschrift
Issue number3-4
StatePublished - 1 Aug 2013
Externally publishedYes

ASJC Scopus subject areas

  • Mathematics (all)


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