Hostname: page-component-78c5997874-s2hrs Total loading time: 0 Render date: 2024-11-10T20:08:17.615Z Has data issue: false hasContentIssue false
  • English
  • Français

THE G-HILBERT SCHEME FOR

Published online by Cambridge University Press:  25 August 2010

OSKAR KĘDZIERSKI
OSKAR KĘDZIERSKI*
Affiliation:
Institute of Mathematics, Warsaw University, ul. Banacha 2, 02-097 Warszawa, Poland e-mail: oskar@mimuw.edu.pl
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.

Following Craw, Maclagan, Thomas and Nakamura's works[2, 7] on Hilbert schemes for abelian groups, we give an explicit description of theHilbGℂ3 scheme for G = 〈diag(ϵ, ϵa, ϵr−a)〉 by a classification of all G-sets. We describe how the combinatorial properties of the fan of HilbGℂ3 relates to the Euclidean algorithm.

Keywords

Primary 14E16Secondary 14C0514B05
Type
Research Article
Information
Glasgow Mathematical Journal , Volume 53 , Issue 1 , January 2011 , pp. 115 - 129
Copyright
Copyright © Glasgow Mathematical Journal Trust 2010

References

REFERENCES

1.Craw, A., Maclagan, D. and Thomas, R. R., Moduli of McKay quiver representations. I. The coherent component, Proc. Lond. Math. Soc. (3) 95 (1) (2007), 179–198.CrossRefGoogle Scholar
2.Craw, A., Maclagan, D. and Thomas, R. R., Moduli of McKay quiver representations. II. Gröbner basis techniques, J. Algebra 316 (2) (2007), 514–535.CrossRefGoogle Scholar
3.Craw, A. and Reid, M., How to calculate A-Hilb ℂ3, in Geometry of toric varieties, vol. 6, Séminaires et Congres (Laurent, Bonavero, Editor) (Society for Mathematics France, Paris, 2002), pp. 129–154.Google Scholar
4.Kȩdzierski, O., Cohomology of the G-Hilbert scheme for , Serdica Math. J. 30 (2–3) (2004), 293–302.Google Scholar
5.Kidoh, R., Hilbert schemes and cyclic quotient surface singularities, Hokkaido Math. J. 30 (1) (2001), 91–103.CrossRefGoogle Scholar
6.Morrison, D. R. and Stevens, G., Terminal quotient singularities in dimensions three and four, Proc. Amer. Math. Soc. 90 (1) (1984), 15–20.CrossRefGoogle Scholar
7.Nakamura, I., Hilbert schemes of abelian group orbits, J. Algebraic Geom. 10 (4) (2001), 757–779.Google Scholar
8.Sebestean, M., Smooth toric G-Hilbert schemes via G-graphs, C. R. Math. Acad. Sci. Paris 344 (2) (2007), 115–119.CrossRefGoogle Scholar