Hilbert functions of fat point subschemes of the plane: the Two-fold Way
نویسندگان
چکیده
Two approaches for determining Hilbert functions of fat point subschemes of P2 are demonstrated. A complete determination of the Hilbert functions which occur for 9 double points is given using the first approach, extending results obtained in a previous paper using the second approach. In addition the second approach is used to obtain a complete determination of the Hilbert functions for n ≥ 9m-multiple points for everym if the points are smooth points of an irreducible plane cubic curve. Additional results are obtained using the first approach for n ≥ 9 double points when the points lie on an irreducible cubic (but now are not assumed to be smooth points of the cubic).
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