Counting Singular Plane Curves Via Hilbert Schemes
Algebraic Geometry
2007-05-23 v2
Abstract
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<n<9.
Keywords
Cite
@article{arxiv.math/0011214,
title = {Counting Singular Plane Curves Via Hilbert Schemes},
author = {Heather Russell},
journal= {arXiv preprint arXiv:math/0011214},
year = {2007}
}
Comments
examples added, some results strengthened, some minor errors corrected, some expositional changes