Enumeration of singular algebraic curves

Details Enumeration of singular algebraic curves Enumeration of singular algebraic curves

2004-07-21

arxiv.org/abs/math/0407358v4

Israel Journal of Math. 155 (2006), pp1-56

Mathematics

Algebraic Geometry

An updated version of the published paper. Here we correct some numerical errors (thanks to M.Kazarian). We also simplify some

Scientific paper

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 a recursive 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 the knowledge of all the possible deformations of a given singularity.

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