2011/01/26 by Geramita, A. V., Harbourne, B., Migliore, J.
#13D40 #14C20 #14M07 #14M20 #Algebraic Geometry (math.AG) #Commutative Algebra (math.AC) #FOS: Mathematics
paper · doi:10.48550/arxiv.1101.5140
Two approaches for determining Hilbert functions of fat point subschemes of \mathbb 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≥ 9 m-multiple points for every m 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).