TY - JOUR

T1 - Hypersurfaces of bounded Cohen-Macaulay type

AU - Leuschke, Graham J.

AU - Wiegand, Roger

N1 - Funding Information:
Leuschke's research was supported by an NSF Postdoctoral Fellowship, and Wiegand's was supported by grants from the NSA and the NSF.

PY - 2005/10/1

Y1 - 2005/10/1

N2 - Let R = k[[x0,...,xd]]/(f), where k is a field and f is a non-zero non-unit of the formal power series ring k[[x0,...,xd]]. We investigate the question of which rings of this form have bounded Cohen-Macaulay type, that is, have a bound on the multiplicities of the indecomposable maximal Cohen-Macaulay modules. As with finite Cohen-Macaulay type, if the characteristic is different from two, the question reduces to the one-dimensional case: The ring R has bounded Cohen-Macaulay type if and only if R≅k[[x0,...,xd]]/ (g+x22 + ⋯ + xd2), where g ∈ k[[x0, x1]] and k[[x0, x1]]/(g) has bounded Cohen-Macaulay type. We determine which rings of the form k[[x0, x 1]]/(g) have bounded Cohen-Macaulay type.

AB - Let R = k[[x0,...,xd]]/(f), where k is a field and f is a non-zero non-unit of the formal power series ring k[[x0,...,xd]]. We investigate the question of which rings of this form have bounded Cohen-Macaulay type, that is, have a bound on the multiplicities of the indecomposable maximal Cohen-Macaulay modules. As with finite Cohen-Macaulay type, if the characteristic is different from two, the question reduces to the one-dimensional case: The ring R has bounded Cohen-Macaulay type if and only if R≅k[[x0,...,xd]]/ (g+x22 + ⋯ + xd2), where g ∈ k[[x0, x1]] and k[[x0, x1]]/(g) has bounded Cohen-Macaulay type. We determine which rings of the form k[[x0, x 1]]/(g) have bounded Cohen-Macaulay type.

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U2 - 10.1016/j.jpaa.2004.12.028

DO - 10.1016/j.jpaa.2004.12.028

M3 - Article

AN - SCOPUS:23344447967

VL - 201

SP - 204

EP - 217

JO - Journal of Pure and Applied Algebra

JF - Journal of Pure and Applied Algebra

SN - 0022-4049

IS - 1-3

ER -