Hostname: page-component-586b7cd67f-t7czq Total loading time: 0 Render date: 2024-11-22T09:57:12.575Z Has data issue: false hasContentIssue false
  • English
  • Français

ON SINGULARITIES OF QUIVER MODULI

Published online by Cambridge University Press:  25 August 2010

MÁTYÁS DOMOKOS
MÁTYÁS DOMOKOS*
Affiliation:
Rényi Institute of Mathematics, Hungarian Academy of Sciences, P.O. Box 127, 1364 Budapest, Hungary e-mail: [email protected]
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.

Any moduli space of representations of a quiver (possibly with oriented cycles) has an embedding as a dense open subvariety into a moduli space of representations of a bipartite quiver having the same type of singularities. A connected quiver is Dynkin or extended Dynkin if and only if all moduli spaces of its representations are smooth.

Keywords

16G2014L24
Type
Research Article
Information
Glasgow Mathematical Journal , Volume 53 , Issue 1 , January 2011 , pp. 131 - 139
Copyright
Copyright © Glasgow Mathematical Journal Trust 2010

References

REFERENCES

1.Adriaenssens, J. and Le Bruyn, L., Local quivers and stable representations, Commun. Algebra 31 (2003), 1777–1797.Google Scholar
2.Bardsley, P. and Richardson, R. W., Étale slices for algebraic transformation groups in characteristic p, Proc. Lond. Math. Soc., Ser. 3, 51 (1985), 295–317.Google Scholar
3.Bocklandt, R., Smooth quiver representation spaces, J. Algebra 253 (2000), 296–313.CrossRefGoogle Scholar
4.Chindris, C., Orbit semi-groups and the representation type of quivers, J. Pure Appl. Algebra 213 (2009), 1418–1429.CrossRefGoogle Scholar
5.Derksen, H. and Weyman, J., On the Littlewood–Richardson polynomials, J. Algebra 255 (2002), 247–257.CrossRefGoogle Scholar
6.Derksen, H. and Weyman, J., The combinatorics of quiver representations, preprint arXiv:math.RT/0608288.Google Scholar
7.Domokos, M., Relative invariants of 3 × 3 matrix triples, Lin. Multilin. Algebra 47 (2000), 175–190.Google Scholar
8.Domokos, M., Kuzmin, S. G. and Zubkov, A. N., Rings of matrix invariants in positive characteristic, J. Pure Appl. Algebra 176 (2002), 61–80.Google Scholar
9.Domokos, M. and Lenzing, H., Moduli spaces for representations of concealed-canonical algebras, J. Algebra 251 (2002), 1–24.CrossRefGoogle Scholar
10.Domokos, M. and Zubkov, A. N., Semi-invariants of quivers as determinants, Transform. Groups 6 (1) (2001), 9–24.Google Scholar
11.Domokos, M. and Zubkov, A. N., Semisimple representations of quivers in characteristic p, Algebra Represent. Theory 5 (2002), 305–317.CrossRefGoogle Scholar
12.Engel, J. and Reineke, M., Smooth models of quiver moduli, Math. Z. 262 (2009), 817–848.CrossRefGoogle Scholar
13.Kac, V. G., Infinite root systems, representations of graphs and invariant theory, Invent. Math. 56 (1980), 57–92.CrossRefGoogle Scholar
14.King, A. D., Moduli of representations of finite dimensional algebras, Q. J. Math. Oxford, 45 (2) (1994), 515–530.CrossRefGoogle Scholar
15.Kraft, H. and Riedtmann, Ch., Geometry of representations of quivers, in Representations of algebras (Webb, P., Editor), London Mathematical Society Lecture Note Series, vol. 116 (1986), 109–145.Google Scholar
16.Le Bruyn, L. and Procesi, C., Semisimple representations of quivers, Trans. Amer. Math. Soc. 317 (1990), 585–598.Google Scholar
17.Le Bruyn, L. and Teranishi, Y., Matrix invariants and complete intersections, Glasgow Math. J. 32 (1990), 227–229.CrossRefGoogle Scholar
18.Luna, D., Slices étales, Bull. Soc. Math. France 33 (1973), 81–105.Google Scholar
19.Newstead, P. E., Introduction to moduli problems and orbit spaces, Tata Institute of Fundamental Research Lectures on Mathematics and Physics, vol. 51 (Narosa Publishing House, New Delhi, 1978).Google Scholar
20.Reineke, M., The use of geometric and quantum group techniques for wild quivers, Fields Inst. Commun. 40 (2004), 365–390.Google Scholar
21.Schofield, A., General representations of quivers, Proc. Lond. Math. Soc. 65 (3) (1992), 46–64.CrossRefGoogle Scholar
22.Skowroński, A. and Weyman, J., The algebras of semi-invariants of quivers, Transform. Groups 5 (4) (2000), 361–402.CrossRefGoogle Scholar