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