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arXiv · 1609.04650

Green's theorem and Gorenstein sequences

Jeaman Ahn·Juan C. Migliore·Yong-Su Shin
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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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Jeaman Ahn, Juan C. Migliore, Yong-Su Shin. 2016-09-15. Green's theorem and Gorenstein sequences. https://arxiv.org/abs/1609.04650

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