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Green's theorem and Gorenstein sequences
Ahn, J.,Migliore, J.C.,Shin, Y.S. North-Holland Pub. Co 2018 Journal of pure and applied algebra Vol.222 No.2
We study consequences, for a standard graded algebra, of extremal behavior in Green's Hyperplane Restriction Theorem. First, we extend his Theorem 4 from the case of a plane curve to the case of a hypersurface in a linear space. Second, assuming a certain Lefschetz condition, we give a connection to extremal behavior in Macaulay's theorem. We apply these results to show that (1,19,17,19,1) is not a Gorenstein sequence, and as a result we classify the sequences of the form (1,a,a-2,a,1) that are Gorenstein sequences.