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Singularities, Representation of Algebras, and Vector Bundles

Proceedings of a Symposium held in Lambrecht/Pfalz, Fed.Rep. of Germany, Dec. 13-17, 1985

  • Conference proceedings
  • © 1987

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Editors:
  1. Gert-Martin Greuel
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  2. Günther Trautmann
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Part of the book series: Lecture Notes in Mathematics (LNM, volume 1273)

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Table of contents (21 papers)

  1. Front Matter

    Pages I-XIV
    Download chapter PDF

  2. Survey of vector bundles on curves

    • M. S. Narasimhan
    Pages 1-8

  3. Finite and countable CM-representation type

    • Frank-Olaf Schreyer
    Pages 9-34

  4. Finite dimensional algebras and singularities

    • Idun Reiten
    Pages 35-57

  5. Cohen-Macaulay modules on quadrics

    • Ragnar-Olaf Buchweitz, David Eisenbud, Jürgen Herzog
    Pages 58-116

  6. Monomial curves and obstructions on cyclic quotient singularities

    • Jan Arthur Christophersen
    Pages 117-133

  7. The Grothendieck group of invariant rings and of simple hypersurface singularities

    • Jürgen Herzog, Herbert Sanders
    Pages 134-149

  8. Torsionsfreie Moduln bei Deformation von Kurvensingularitäten

    • Horst Knörrer
    Pages 150-155

  9. Deformation of modules on curves and surfaces

    • C. J. Rego
    Pages 157-167

  10. A characterisation of strictly unimodular plane curve singularities

    • Albert Schappert
    Pages 168-177

  11. Polar curves, resolution of singularities and the filtered mixed hodge structure on the vanishing cohomology

    • Joseph Steenbrink, Steven Zucker
    Pages 178-202

  12. On the betti numbers of the milnor fibre of a certain class of hypersurface singularities

    • D. van Straten
    Pages 203-220

  13. Reflexive modules on cyclic quotient surface singularities

    • J. Wunram
    Pages 221-231

  14. Almost split sequences for ℤ-graded rings

    • Maurice Auslander, Idun Reiten
    Pages 232-243

  15. The auslander-reiten quiver of an isolated singularity

    • Ernst Dieterich
    Pages 244-264

  16. A class of weighted projective curves arising in representation theory of finite dimensional algebras

    • Werner Geigle, Helmut Lenzing
    Pages 265-297

  17. Repetitive categories

    • Dieter Happel
    Pages 298-317

  18. Almost split sequences for some non-classical lattice categories

    • K. W. Roggenkamp
    Pages 318-324

  19. Special instanton bundles and poncelet curves

    • W. Böhmer, G. Trautmann
    Pages 325-336

  20. Groupe de picard des variétés de modules de faisceaux semi-stables sur ℙ2

    • Jean-Marc Drezet
    Pages 337-362
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Keywords

About this book

It is well known that there are close relations between classes of singularities and representation theory via the McKay correspondence and between representation theory and vector bundles on projective spaces via the Bernstein-Gelfand-Gelfand construction. These relations however cannot be considered to be either completely understood or fully exploited. These proceedings document recent developments in the area. The questions and methods of representation theory have applications to singularities and to vector bundles. Representation theory itself, which had primarily developed its methods for Artinian algebras, starts to investigate algebras of higher dimension partly because of these applications. Future research in representation theory may be spurred by the classification of singularities and the highly developed theory of moduli for vector bundles. The volume contains 3 survey articles on the 3 main topics mentioned, stressing their interrelationships, as well as original research papers.

Bibliographic Information

  • Book Title: Singularities, Representation of Algebras, and Vector Bundles

  • Book Subtitle: Proceedings of a Symposium held in Lambrecht/Pfalz, Fed.Rep. of Germany, Dec. 13-17, 1985

  • Editors: Gert-Martin Greuel, Günther Trautmann

  • Series Title: Lecture Notes in Mathematics

  • DOI: https://doi.org/10.1007/BFb0078834

  • Publisher: Springer Berlin, Heidelberg

  • eBook Packages: Springer Book Archive

  • Copyright Information: Springer-Verlag Berlin Heidelberg 1987

  • Softcover ISBN: 978-3-540-18263-4Published: 09 September 1987

  • eBook ISBN: 978-3-540-47851-5Published: 15 November 2006

  • Series ISSN: 0075-8434

  • Series E-ISSN: 1617-9692

  • Edition Number: 1

  • Number of Pages: XVI, 384

  • Topics: Topological Groups, Lie Groups, Algebraic Geometry, Analysis

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