Skip to main content
Log in

The second Brauer-Thrall conjecture for isolated singularities of excellent hypersurfaces

  • Published:
manuscripta mathematica Aims and scope Submit manuscript

Abstract

We give an extension of Dieterich's Theorems on the structure of the Auslander-Reiten quiver of an isolated singularity.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others

References

  • [Au 1] Auslander, M., Functors and morphisms determined by objects, Proc. Conf. Representation Theory, Philadelphia, 1976, New York, Basel 1978, 1–244

  • [Au 2] Auslander, M., Isolated singularities and existence of almost split sequences, Proc. ICRA IV, Springer Lecture Notes in Mathematics No 1178 (1986), 194–241

  • [BGS] Buchweitz, R.O., Greuel, G.M., Schreyer, F.O., Cohen—Macaulay modules on hypersurface singularities II, Inventiones math. 88 (1987), 165–183

    Article  MathSciNet  MATH  Google Scholar 

  • [Di 1] Dieterich, E., Reduction of isolated singularities, Comment. Math. Helvetici 62 (1987), 654–604

    Article  MathSciNet  MATH  Google Scholar 

  • [Di 2] Dieterich, E., The Auslander-Reiten quiver of an isolated singularity, Springer Lecture Notes in Mathematics 1273 (1987), 244–264

    Article  MathSciNet  MATH  Google Scholar 

  • [EG] Evans, E.G., Griffith, P., Syzygies, London Mathematical Society Lecture Note Series, Cambridge 1985

  • [Ei] Eisenbud, D. Homological algebra on a complete intersection with an application to group representations, Trans. AMS 260,1 (1980), 35–64

    Article  MathSciNet  MATH  Google Scholar 

  • [GK] Greuel, G.M., Kröning, H., Simple singularities in positive characteristic, Math. Z. 203 (1990), 339–354

    Article  MathSciNet  MATH  Google Scholar 

  • [HPR] Happel, D., Preiser, U., Ringel, C.M., Vinberg's characterization of Dynkin diagrams using subadditive functions with application to DTr-periodic modules, Proceedings of the third International Conference on Representations of algebras, Carleton University, Ottawa 1979, Springer Lecture Notes in Mathematics 832, 280–294

  • [Kn] Knörrer, H., Cohen Macaulay modules on hypersurface singularities I, Inventiones math. 88 (1987), 153–164

    Article  MathSciNet  MATH  Google Scholar 

  • [Ma] Matsumura, H., Commutative ring theory, Cambridge 1986

  • [Po] Popescu, D., Indecomposable Cohen Macaulay modules and their multiplicities, Trans. AMS 320 (1991)

  • [PR] Popescu, D., Roczen, M., Indecomposable Cohen Macaulay modules and irreducible maps, Compositio Mathematica 76 (1990), 277–294

    MathSciNet  MATH  Google Scholar 

  • [Re] Reiten, L, Finite dimensional algebras and singularities, Springer Lecture Notes in Mathematics 1273 (1987), 35–57

    Article  MathSciNet  MATH  Google Scholar 

  • [Ri] Ringel, C.M., Tame algebras and integral quadratic forms, Springer Lecture Notes in Mathematics 1099 (1984)

  • [Sc] Schreyer, F. O., Finite and countable CM-representation type, Springer Lecture Notes in Mathematics No 1273 (1987), 9–34

    Article  MathSciNet  MATH  Google Scholar 

  • [So] Solberg, Ø., Hypersurface singularities of finite Cohen Macaulay type, Proc. London Math. Soc., III. Ser. 58 (1989), 258–280

    Article  MathSciNet  MATH  Google Scholar 

  • [Yo] Yoshino, Y., Brauer— Thrall type theorem for maximal Cohen-Macaulay modules, J. Math. Soc. Japan 39, 4 (1984), 719–739

    Article  MathSciNet  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Additional information

The first author was supported by a fellowship of the Alexander von Humboldt-Stiftung during the last period of preparation of this paper.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Popescu, D., Roczen, M. The second Brauer-Thrall conjecture for isolated singularities of excellent hypersurfaces. Manuscripta Math 71, 375–383 (1991). https://doi.org/10.1007/BF02568413

Download citation

  • Received:

  • Revised:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF02568413

Keywords

Navigation