Let Z be a curvilinear subscheme in the projective plane, i.e. a zero-dimensional scheme whose embedding dimension at every point of their support is ≤1. We find bounds for the minimum degree of the plane curves on which Z imposes independent conditions and we show that the Hilbert function of Z is maximal for a “generic choice of Z”.
On curvilinear subschemes of P^2
CATALISANO, MARIA VIRGINIA;
1994-01-01
Abstract
Let Z be a curvilinear subscheme in the projective plane, i.e. a zero-dimensional scheme whose embedding dimension at every point of their support is ≤1. We find bounds for the minimum degree of the plane curves on which Z imposes independent conditions and we show that the Hilbert function of Z is maximal for a “generic choice of Z”.
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