Counting Singular Plane Curves Via Hilbert Schemes

Details Counting Singular Plane Curves Via Hilbert Schemes Counting Singular Plane Curves Via Hilbert Schemes

2000-11-24

arxiv.org/abs/math/0011214v2

Mathematics

Algebraic Geometry

examples added, some results strengthened, some minor errors corrected, some expositional changes

Scientific paper

We give a method of counting the number of curves with a given type of singularity in a suitably ample linear series on a smooth surface using punctual Hilbert schemes. The types of singulaties for which our methods suffice include the topological type with local equation x^a +y^b with b-1 < a < 3b+1. We work out the example of curves with the analytic type of singularity with local equation x^2+y^n for 1

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