Enumeration of singular algebraic curves

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8 Scopus citations

Abstract

We enumerate plane complex algebraic curves of a given degree with one singularity of any given topological type. Our approach is to compute the homology classes of the corresponding equisingular strata in the parameter spaces of plane curves. We suggest an inductive procedure, which is based on the intersection theory combined with liftings and degenerations. The procedure computes the homology class in question whenever a given singularity type is defined. Our method does not require knowledge of all the possible deformations of a given singularity, as it was in previously known procedures.

Original languageEnglish
Pages (from-to)1-56
Number of pages56
JournalIsrael Journal of Mathematics
Volume155
DOIs
StatePublished - 27 Dec 2006
Externally publishedYes

ASJC Scopus subject areas

  • Mathematics (all)

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