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Rank One Maximal Cohen-Macaulay Modules Over Singularities of Type Y 31 + Y 32 + Y 33 + Y 34

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Commutative Algebra, Singularities and Computer Algebra

Part of the book series: NATO Science Series ((NAII,volume 115))

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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

  1. M.F. Atiyah. Vector bundles over an elliptic curve. Proc. London Math. Soc. 7(3) (1957), 415-452.

    MathSciNet  Google Scholar 

  2. M. Auslander, S. Ding, O. Solberg. Liftings and weak liftings of modules. J. of Algebra, 156 (1993), 273-317.

    Article  MathSciNet  MATH  Google Scholar 

  3. 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.

    Google Scholar 

  4. Matrix factorizations of homogeneous polynomials. Lecture Notes in Math., 1352 (1988), 1-33.

    Article  MathSciNet  Google Scholar 

  5. M. Cipu. Generalized Cohen-Macaulay modules over rings with approximation property. Ann. Univ. Ferrara, 37 (1991), 85-93.

    MathSciNet  MATH  Google Scholar 

  6. M. Cipu. An explicit study of l-sequences. Comm, in Algebra, 24 (1996), 2249-2269.

    Article  MathSciNet  MATH  Google Scholar 

  7. M. Cipu, J. Herzog, D. Popescu. Indecomposable generalized Cohen-Macaulay modules. Trans. AMS, 342 (1994), 107-136.

    Article  MathSciNet  MATH  Google Scholar 

  8. M. Cipu, M. Fiorentini. Ubiquity of relative regular sequences and proper sequences. K- Theory, 8 (1994), 81-106.

    Article  MathSciNet  MATH  Google Scholar 

  9. D. Eisenbud On the resiliency of determinantal ideals, in: Commutative Algebra and Combinatorics, Adv. Stud. Pure Math. Vol.11, 1987, 29-38.

    Google Scholar 

  10. D. Eisenbud. Homological algebra with an application to group representations. Trans. Amer. Math. Soc. 260 (1980), 35-64.

    Article  MathSciNet  MATH  Google Scholar 

  11. 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.

    MathSciNet  Google Scholar 

  12. 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.

  13. 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.

    Google Scholar 

  14. C.P. Kahn, Reflexive modules on minimally elliptic singularities. Math. Ann. 285 (1989), 141– 160.

    Article  MathSciNet  MATH  Google Scholar 

  15. . H. Knörrer. Cohen-Macaulay modules on hypersurface singularities 1. Invent. Math., 88 (1987), 153-164.

    Article  MathSciNet  MATH  Google Scholar 

  16. 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.

    Google Scholar 

  17. R. Laza, G. Pfister, D. Popescu. Maximal Cohen-Macaulay modules over the cone of an elliptic curve. J. of Algebra, 253 (2002), 209–236.

    Article  MathSciNet  MATH  Google Scholar 

  18. G. Pfister, D. Popescu. Deformations of maximal Cohen-Macaulay modules. Math. Z. 223 (1996), 309–332.

    MathSciNet  MATH  Google Scholar 

  19. D. Popescu, Maximal Cohen-Macaulay modules over isolated singularities. J. of Algebra, 178 (1995), 710–732.

    Article  MATH  Google Scholar 

  20. Y. Yoshino. Cohen-Macaulay modules over Cohen-Macaulay rings. London Math. Soc. Lecture Note Ser. Vol.146, Cambridge, 1990.

    Google Scholar 

  21. Y Yoshino. Tensor product of matrix factorizations. Nagoya Math. J. 152 (1998), 39–56.

    MathSciNet  MATH  Google Scholar 

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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

  • Publisher Name: Springer, Dordrecht

  • Print ISBN: 978-1-4020-1487-1

  • Online ISBN: 978-94-007-1092-4

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