Enumeration of uni-singular algebraic hypersurfaces

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3 Scopus citations

Abstract

We enumerate complex algebraic hypersurfaces in n, of a given (high) degree with one singular point of a given singularity type. Our approach is to compute the (co)homology classes of the corresponding equisingular strata in the parameter space of hypersurfaces. We suggest an inductive procedure, based on an intersection theory combined with liftings and degenerations. The procedure computes the (co)homology class in question, whenever a given singularity type is properly defined and the stratum possesses good geometric properties. We consider in detail the generalized Newton-non-degenerate singularities. We also give examples of enumeration in some other cases.

Original languageEnglish
Pages (from-to)623-668
Number of pages46
JournalProceedings of the London Mathematical Society
Volume96
Issue number3
DOIs
StatePublished - 1 Jan 2008
Externally publishedYes

ASJC Scopus subject areas

  • Mathematics (all)

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