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math.AG2000
Toric Varieties in Hilbert Schemes
Heather Russell
For an arbitrary field K, let I be an ideal in the ring K[[x,y]] expressible as a polynomial in either the pair of ideals (x, y^4) and (x,y) or the pair (x,y^3) and (x^2, y). Let G…
math.AG2000
Alignment Correspondences
Heather Russell
We study correspondences of zero-dimensional subschemes of a smooth variety X "aligned" in the same way in inside the appropriate product of Hilbert schemes. We show that such corr…
math.AG2000
Counting Singular Plane Curves Via Hilbert Schemes
Heather Russell
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 o…