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arXiv · 1307.6206

Non-Gorenstein isolated singularities of graded countable Cohen-Macaulay type

Branden Stone
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Abstract

In this paper we show a partial answer the a question of C. Huneke and G. Leuschke (2003): Let R be a standard graded Cohen-Macaulay ring of graded countable Cohen-Macaulay representation type, and assume that R has an isolated singularity. Is R then necessarily of graded finite Cohen-Macaulay representation type? In particular, this question has an affirmative answer for standard graded non-Gorenstein rings as well as for standard graded Gorenstein rings of minimal multiplicity. Along the way, we obtain a partial classification of graded Cohen-Macaulay rings of graded countable Cohen-Macaulay type.

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Branden Stone. 2013-07-23. Non-Gorenstein isolated singularities of graded countable Cohen-Macaulay type. https://arxiv.org/abs/1307.6206

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