Milnor numbers of projective hypersurfaces with isolated singularities

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Let V be a projective hypersurface of fixed degree and dimension which has only isolated singular points. We show that, if the sum of the Milnor numbers at the singular points of V is large, then V cannot have a point of large multiplicity, unless V is a cone. As an application, we give an affirmative answer to a conjecture of Dimca and Papadima.

Original languageEnglish (US)
Pages (from-to)1525-1548
Number of pages24
JournalDuke Mathematical Journal
Issue number8
StatePublished - Jun 2014
Externally publishedYes

All Science Journal Classification (ASJC) codes

  • General Mathematics


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