Green's theorem and Gorenstein sequences

2016/09/15 by Ahn, Jeaman, Migliore, Juan C., Shin, Yong-Su · 1 citation
#Commutative Algebra (math.AC) #FOS: Mathematics

paper · doi:10.48550/arxiv.1609.04650

Abstract

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.

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