Green's theorem and Gorenstein sequences |
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Authors: | Jeaman Ahn Juan C. Migliore Yong-Su Shin |
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Affiliation: | 1. Department of Mathematics Education, Kongju National University, 182, Shinkwan-dong, Kongju, Chungnam 314-701, Republic of Korea;2. Department of Mathematics, University of Notre Dame, Notre Dame, IN 46556, USA;3. Department of Mathematics, Sungshin Women''s University, Seoul, 136-742, Republic of Korea |
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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 is not a Gorenstein sequence, and as a result we classify the sequences of the form that are Gorenstein sequences. |
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Keywords: | Primary 13D40 secondary 13H10 14C20 |
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