Abstract
We describe, by matrix factorizations, the rank one graded maximal Cohen-Macaulay modules over the hypersurface Y 1 3+Y 2 3+ Y 3 3 + Y 4 3.
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References
M.F. Atiyah. Vector bundles over an elliptic curve. Proc. London Math. Soc. 7(3) (1957), 415-452.
M. Auslander, S. Ding, O. Solberg. Liftings and weak liftings of modules. J. of Algebra, 156 (1993), 273-317.
J. Backelin, J. Herzog. On Ulrich modules over hypersurface rings. Proceedings of the Mi- croprogram on Comm. Alg. at MSRI, Berkeley/CA(USA), 1989, Publ. Math. Sci. Res. Inst. 15 (1989), 63-68.
Matrix factorizations of homogeneous polynomials. Lecture Notes in Math., 1352 (1988), 1-33.
M. Cipu. Generalized Cohen-Macaulay modules over rings with approximation property. Ann. Univ. Ferrara, 37 (1991), 85-93.
M. Cipu. An explicit study of l-sequences. Comm, in Algebra, 24 (1996), 2249-2269.
M. Cipu, J. Herzog, D. Popescu. Indecomposable generalized Cohen-Macaulay modules. Trans. AMS, 342 (1994), 107-136.
M. Cipu, M. Fiorentini. Ubiquity of relative regular sequences and proper sequences. K- Theory, 8 (1994), 81-106.
D. Eisenbud On the resiliency of determinantal ideals, in: Commutative Algebra and Combinatorics, Adv. Stud. Pure Math. Vol.11, 1987, 29-38.
D. Eisenbud. Homological algebra with an application to group representations. Trans. Amer. Math. Soc. 260 (1980), 35-64.
V. Ene, D. Popescu. Steps in the classification of Cohen-Macaulay modules over singularities of type Xt+ Y3. Algebra and Representation Theory, 2(2) (1999), 35-64.
G.-M. Greuel, G. Pfister, and H. Schönemann. SINGULAR2.0. A Computer Algebra System for Polynomial Computations. Centre for Computer Algebra, University of Kaiserslautern (2001). http://www.singular.uni-kl.de.
J. Herzog, M. Kiihl. Maximal Cohen-Macaulay modules over Gorenstein rings and Bourbaki sequences, in: Commutative Algebra and Combinatorics, Adv. Stud. Pure Math. Vol. 11,1987, 65–92.
C.P. Kahn, Reflexive modules on minimally elliptic singularities. Math. Ann. 285 (1989), 141– 160.
. H. Knörrer. Cohen-Macaulay modules on hypersurface singularities 1. Invent. Math., 88 (1987), 153-164.
R. Laza, L. O’Carroll, D. Popescu. Maximal Cohen-Macaulay modules over Y 1 3+ ... + Y n 3 with few generators. Math. Reports 3(53)2 (2001), 177–185.
R. Laza, G. Pfister, D. Popescu. Maximal Cohen-Macaulay modules over the cone of an elliptic curve. J. of Algebra, 253 (2002), 209–236.
G. Pfister, D. Popescu. Deformations of maximal Cohen-Macaulay modules. Math. Z. 223 (1996), 309–332.
D. Popescu, Maximal Cohen-Macaulay modules over isolated singularities. J. of Algebra, 178 (1995), 710–732.
Y. Yoshino. Cohen-Macaulay modules over Cohen-Macaulay rings. London Math. Soc. Lecture Note Ser. Vol.146, Cambridge, 1990.
Y Yoshino. Tensor product of matrix factorizations. Nagoya Math. J. 152 (1998), 39–56.
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Ene, V., Popescu, D. (2003). Rank One Maximal Cohen-Macaulay Modules Over Singularities of Type Y 31 + Y 32 + Y 33 + Y 34 . In: Herzog, J., Vuletescu, V. (eds) Commutative Algebra, Singularities and Computer Algebra. NATO Science Series, vol 115. Springer, Dordrecht. https://doi.org/10.1007/978-94-007-1092-4_8
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DOI: https://doi.org/10.1007/978-94-007-1092-4_8
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