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The paper [10] raised the question of what the possible Hilbert functions are for fat point subschemes of the form 2p1+...+2pr, for all possible choices ofr distinct points in ℙ2. We study this problem forr points in ℙ2 over an algebraically closed fieldk of arbitrary characteristic in case eitherr ≤ 8 or the points lie on a (possibly reducible) conic. In either case, it follows...
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