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Baciu, Corina; Ene, Viviana; Pfister, Gerhard; Popescu, Dorin

doi:10.1016/j.jalgebra.2005.01.001

Journal of Algebra

2005

DOI: 10.1016/j.jalgebra.2005.01.001

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Rank 2 Cohen–Macaulay modules over singularities of type x13+x23+x33+x43

Corina Baciu

Viviana Ene

Gerhard Pfister

et al.

Abstract: We describe, by matrix factorizations, all graded, rank 2, maximal Cohen-Macaulay modules over singularities of type x 3 1 + x 3 2 + x 3 3 + x 3 4 .

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Rank 2 arithmetically Cohen–Macaulay bundles on a nonsingular cubic surface

Faenzi

2008

Journal of Algebra

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Rank 2 indecomposable arithmetically Cohen-Macaulay bundles E on a nonsingular cubic surface X in P 3 are classified, by means of the possible forms taken by the minimal graded free resolution of E over P 3 . The admissible values of the Chern classes of E are listed and the vanishing locus of a general section of E is studied.Properties of E such as slope (semi)stability and simplicity are investigated; the number of relevant families is computed together with their dimension.

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Rank 2 arithmetically Cohen–Macaulay bundles on a nonsingular cubic surface

Faenzi

2008

Journal of Algebra

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Factoring the adjoint and maximal Cohen-Macaulay modules over the generic determinant

Buchweitz¹,

Leuschke²

2007

ajm

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Abstract. A question of Bergman [3] asks whether the adjoint of the generic square matrix over a field can be factored nontrivially as a product of square matrices. We show that such factorizations indeed exist over any coefficient ring when the matrix has even size. Establishing a correspondence between such factorizations and extensions of maximal Cohen-Macaulay modules over the generic determinant, we exhibit all factorizations where one of the factors has determinant equal to the generic determinant. The classification shows not only that the Cohen-Macaulay representation theory of the generic determinant is wild in the tame-wild dichotomy, but that it is quite wild: even in rank two, the isomorphism classes cannot be parametrized by a finite-dimensional variety over the coefficients. We further relate the factorization problem to the multiplicative structure of the Ext-algebra of the two nontrivial rank-one maximal Cohen-Macaulay modules and determine it completely.

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Rank 2 Cohen–Macaulay modules over singularities of type x13+x23+x33+x43

Abstract: We describe, by matrix factorizations, all graded, rank 2, maximal Cohen-Macaulay modules over singularities of type x 3 1 + x 3 2 + x 3 3 + x 3 4 .

Cited by 2 publications

References 7 publications

Rank 2 arithmetically Cohen–Macaulay bundles on a nonsingular cubic surface

Rank 2 arithmetically Cohen–Macaulay bundles on a nonsingular cubic surface

Factoring the adjoint and maximal Cohen-Macaulay modules over the generic determinant

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