Journal of Algebraic Geometry

Journal of Algebraic Geometry

Online ISSN 1534-7486; Print ISSN 1056-3911



A characterization of quasi-homogeneous complete intersection singularities

Author: Henrik Vosegaard
Journal: J. Algebraic Geom. 11 (2002), 581-597
Published electronically: March 13, 2002
MathSciNet review: 1894939
Full-text PDF

Abstract | References | Additional Information

Abstract: It is well-known that quasi-homogeneity is characterized by equality of the Milnor and Tjurina numbers for isolated complex analytic hypersurface singularities and for certain low-dimensional singularities. We prove that this characterization extends to any complex isolated complete intersection singularity of positive dimension.

References [Enhancements On Off] (What's this?)

  • [BG] R.-O. Buchweitz and G.-M. Greuel, The Milnor number and deformations of complex curve singularities, Invent. Math. 58 (1980), 241-281.
  • [G1] G.-M. Greuel, Der Gauß-Manin-Zusammenhang isolierter Singularitäten von vollständigen Durchschnitten, Math. Ann. 214 (1975), 235-266.
  • [G2] G.-M. Greuel, Dualität in der lokalen Kohomologie isolierter Singularitäten, Math. Ann. 250 (1980), 157-173.
  • [G3] G.-M. Greuel, On deformation of curves and a formula of Deligne, Algebraic Geometry, proceedings La Rábida 1981, LNM 961, Springer-Verlag, 1982, pp. 141-168.
  • [GMP] G.-M. Greuel, B. Martin and G. Pfister, Numerische Charakterisierung Quasihomogener Gorenstein-Kurvensingularitäten, Math. Nachr. 124 (1985), 123-131.
  • [L] E. Looijenga, Isolated singular points on complete intersections, London Math. Soc. LNS 77, Cambridge Univ. Press, 1984.
  • [LS] E. Looijenga and J. Steenbrink, Milnor number and Tjurina number of complete intersections, Math. Ann. 271 (1985), 121-124.
  • [Sa] K. Saito, Quasihomogene isolierte Singularitäten von Hyperflächen, Invent. Math. 14 (1971), 123-142.
  • [Se] J.-P. Serre, Groupes algébriques et corps de classes, Hermann, 1959.
  • [St] J.H.M. Steenbrink, Mixed Hodge structures associated with isolated singularities, Proc. Symp. Pure Math., vol. 40, 1983, pp. 513-536.
  • [SW] G. Scheia and H. Wiebe, Über Derivationen in isolierten Singularitäten auf vollständigen Durchschnitten, Math. Ann. 225 (1977), 161-171.
  • [V1] H. Vosegaard, Generalized Tjurina numbers of an isolated complete intersection singularity, European Singularities Network Preprints Archive 1998 (to appear in Math. Ann.).
  • [V2] H. Vosegaard, A characterization of quasi-homogeneous purely elliptic complete intersection singularities, Compositio Math. 124 (2000), 111-121.
  • [W] J. Wahl, A characterization of quasi-homogeneous Gorenstein surface singularities, Compositio Math. 55 (1985), 269-288.

Additional Information

Henrik Vosegaard
Affiliation: Department of Mathematics, Aarhus University, Ny Munkegade, DK-8000 Aarhus C, Denmark

Received by editor(s): July 5, 2000
Received by editor(s) in revised form: October 10, 2000
Published electronically: March 13, 2002

Journal of Algebraic Geometry
The Journal of Algebraic Geometry
is sponsored by the Department of Mathematical Sciences
of Tsinghua University
and is distributed by the American Mathematical Society
for University Press, Inc.
Online ISSN 1534-7486; Print ISSN 1056-3911
© 2017 University Press, Inc.
AMS Website