Non-Gorenstein isolated singularities of graded countable Cohen-Macaulay type
Commutative Algebra
2013-07-24 v1
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.
Keywords
Cite
@article{arxiv.1307.6206,
title = {Non-Gorenstein isolated singularities of graded countable Cohen-Macaulay type},
author = {Branden Stone},
journal= {arXiv preprint arXiv:1307.6206},
year = {2013}
}
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15 Pages