Hostname: page-component-586b7cd67f-t7czq Total loading time: 0 Render date: 2024-11-23T01:07:16.482Z Has data issue: false hasContentIssue false
  • English
  • Français

ON THE GEOMETRY OF ORBIT CLOSURES FOR REPRESENTATION-INFINITE ALGEBRAS

Published online by Cambridge University Press:  30 March 2012

CALIN CHINDRIS
CALIN CHINDRIS*
Affiliation:
Mathematics Department, University of Missouri, Columbia, MO 65211, USA e-mail: chindrisc@missouri.edu
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

For the Kronecker algebra, Zwara found in [14] an example of a module whose orbit closure is neither unibranch nor Cohen-Macaulay. In this paper, we explain how to extend this example to all representation-infinite algebras with a preprojective component.

Keywords

Primary 16G30Secondary 16G2016R30
Type
Research Article
Information
Glasgow Mathematical Journal , Volume 54 , Issue 3 , September 2012 , pp. 629 - 636
Copyright
Copyright © Glasgow Mathematical Journal Trust 2012

References

REFERENCES

1.Assem, I., Simson, D. and Skowroński, A., Elements of the representation theory of associative algebras. Vol. 1: Techniques of representation theory, London Mathematical Society Student Texts, vol. 65 (Cambridge University Press, Cambridge, 2006).CrossRefGoogle Scholar
2.Bobiński, G. and Skowroński, A., Geometry of modules over tame quasi-tilted algebras, Colloq. Math. 79 (1) (1999), 85–118.CrossRefGoogle Scholar
3.Bongartz, K., Algebras and quadratic forms, J. London Math. Soc. (2) 28 (3) (1983), 461–469.CrossRefGoogle Scholar
4.Bongartz, K., Minimal singularities for representations of Dynkin quivers, Comment. Math. Helv. 69 (4) (1994), 575–611.CrossRefGoogle Scholar
5.Chindris, C., Geometric characterizations of the representation type of hereditary algebras and of canonical algebras, Adv. Math. 228 (3) (2011), 1405–1434.CrossRefGoogle Scholar
6.Derksen, H. and Weyman, J., The combinatorics of quiver representations. Preprint available at arXiv.math.RT/0608288 (2006).Google Scholar
7.Happel, D. and Vossieck, D., Minimal algebras of infinite representation type with preprojective component, Manuscripta Math. 42 (2–3) (1983), 221–243.CrossRefGoogle Scholar
8.Keller, B., A-infinity algebras in representation theory, Representations of Algebra, vols. I and II (Beijing Norm. Univ. Press, Beijing, 2002), 74–86.Google Scholar
9.Keller, B., A-infinity algebras, modules and functor categories, Trends in Representation Theory of Algebras and Related Topics, Contemp. Math., vol. 406 (Amer. Math. Soc., Providence, RI, 2006), 67–93.Google Scholar
10.Ringel, C. M., The braid group action on the set of exceptional sequences of a hereditary Artin algebra. Abelian Group Theory and Related Topics (Oberwolfach, 1993), Contemp. Math., vol. 171 (Amer. Math. Soc., Providence, RI, 1994), 339–352.CrossRefGoogle Scholar
11.Simson, D. and Skowroński, A., Elements of the representation theory of associative algebras. Vol. 2, London Mathematical Society Student Texts, vol. 71 (Cambridge University Press, Cambridge, 2007). Tubes and concealed algebras of Euclidean type.Google Scholar
12.Zwara, G., Smooth morphisms of module schemes, Proc. London Math. Soc. (3) 84 (3) (2002), 539–558.CrossRefGoogle Scholar
13.Zwara, G., Unibranch orbit closures in module varieties, Ann. Sci. École Norm. Sup. (4) 35 (6) (2002), 877–895.CrossRefGoogle Scholar
14.Zwara, G., An orbit closure for a representation of the Kronecker quiver with bad singularities, Colloq. Math. 97 (1) (2003), 81–86.CrossRefGoogle Scholar