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arXiv · 1301.3593

Super-stretched and graded countable Cohen-Macaulay type

Branden Stone
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Abstract

We define what it means for a Cohen-Macaulay ring to to be super-stretched and show that Cohen-Macaulay rings of graded countable Cohen-Macaulay type are super-stretched. We use this result to show that rings of graded countable Cohen-Macaulay type, and positive dimension, have possible h-vectors (1), (1,n), or (1,n,1). Further, one dimensional standard graded Gorenstein rings of graded countable type are shown to be hypersurfaces; this result is not known in higher dimensions. In the non-Gorenstein case, rings of graded countable Cohen-Macaulay type of dimension larger than 2 are shown to be of minimal multiplicity.

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Branden Stone. 2013-07-23. Super-stretched and graded countable Cohen-Macaulay type. https://arxiv.org/abs/1301.3593

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