Singularities, Representation of Algebras, and Vector Bundles

1. Front Matter

   Pages I-XIV

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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

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.

• Lattice
• Representation theory
• cohomology
• homology
• moduli space
• vector bundle

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