Cohen-Macaulay modules on hypersurface singularities I

Knörrer, Horst

doi:10.1007/bf01405095

Cited by 273 publications

(180 citation statements)

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“…Looking at the entry 1Y 1 of I d we see that this is a contradiction by (5). Thus, s j 2 for all 1 % j % q and d 2q.…”

Section: Infinitesimal Deformations Of Modules Over K[[x]]/(x T )mentioning

confidence: 92%

“…The problem of Thom-Sebastiani type for the categories of maximal Cohen-Macaulay modules (see [4]) means studying the category of maximal Cohen-Macaulay modules over KxY yaf g in connection with the categories of maximal Cohen-Macaulay modules over Kxaf and Kyag, respectively. A very special case of this type of problem appears in Knörrers paper [5], where the hypersurface singularities of type f y 2 , that is g y 2 , are studied. If char K j 2, then every maximal Cohen-Macaulay R HH KxY yaf y 2 -module is a direct summand in the first syzygy over R HH of a certain maximal Cohen-Macaulay R X Kxaf -module (see [5]).…”

mentioning

confidence: 99%

“…A very special case of this type of problem appears in Knörrers paper [5], where the hypersurface singularities of type f y 2 , that is g y 2 , are studied. If char K j 2, then every maximal Cohen-Macaulay R HH KxY yaf y 2 -module is a direct summand in the first syzygy over R HH of a certain maximal Cohen-Macaulay R X Kxaf -module (see [5]). This result was very useful for proving that a hypersurface over an algebraically closed field of characteristic j 2 is simple if and only if it has a finite Cohen-Macaulay representation type (see [5], [2]).…”

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confidence: 99%

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Infinitesimal module deformations in the Thom-Sebastiani Problem

Enescu

Pfister

Popescu

1997

Archiv der Mathematik

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“…Looking at the entry 1Y 1 of I d we see that this is a contradiction by (5). Thus, s j 2 for all 1 % j % q and d 2q.…”

Section: Infinitesimal Deformations Of Modules Over K[[x]]/(x T )mentioning

confidence: 92%

mentioning

confidence: 99%

mentioning

confidence: 99%

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Infinitesimal module deformations in the Thom-Sebastiani Problem

Enescu

Pfister

Popescu

1997

Archiv der Mathematik

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“…[K2,Theorem 3.1].) On the other hand, Herzog and Popescu [HP] had considered the same problem for the particular case R 2 = K [[yι]]/(yl) and they call the problem "Thom-Sebastiani problem".…”

Section: ]/(F + G) Actually If λ 2 = K[[yι])l{yl) or If R 2 = K[[y Umentioning

confidence: 99%

Tensor products of matrix factorizations

Yoshino

1998

Nagoya Mathematical Journal

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Abstract. Let K be a field and let / 6 K[ [xι,x 2 , . ,x r ]] and g 6 #[[2/1,2/2, , y s ]] be non-zero and non-invertible elements. If X (resp. Y) is a matrix factorization of / (resp. g), then we can construct the matrix factorization X §> Y of /-+• g over K [[xiyX2, -> ,x r ,yi,y2, -,ys]]i which we call the tensor product of X and y.After showing several general properties of tensor products, we will prove theorems which give bounds for the number of indecomposable components in the direct decomposition of X < §> Y.

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“…The study of indecomposable finite modules over Artinian rings was extended in recent years to the study of indecomposable maximal Cohen-Macaulay modules over Cohen-Macaulay local rings (see, e.g., [2,4,9,12,19,27,32]). So representation theory has achieved a remarkable progress in the attempt to generalize the methods and results known for Artinian rings to higher dimensional local rings.…”

Section: Introductionmentioning

confidence: 99%