Parametrizations of Ideals in K[x,y] and K[x,y,z]

Details Parametrizations of Ideals in K[x,y] and K[x,y,z] Parametrizations of Ideals in K[x,y] and K[x,y,z]

2012-01-13

arxiv.org/abs/1201.2835v1

Journal of Algebra 346, pp. 1--30, (2011)

Mathematics

Algebraic Geometry

23 pages

Scientific paper

We parametrize the affine space of Artinian affine ideals of K[x,y] which have a given initial ideal with respect to the degree reverse lexicographic term order. The fact that the term order is degree compatible allows us to extend the parametrization to the projective case, namely zero-dimensional subschemes of the projective plane, with some extra assumption and to determine the Betti strata of these Groebner cells. This allows us to prove a formula due to A. Iarrobino for the codimension of the Betti strata of codimension two punctual schemes in the projective plane.

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