Differential Invariance of Multiplicity of Analytic Varieties.
Y.-N. Gau, J. Lipman (1983)
Inventiones mathematicae
Hélène Maugendre (1998)
Annales de la Faculté des sciences de Toulouse : Mathématiques
P. Jaworski (1986)
Inventiones mathematicae
Joseph H. M. Steenbrink (1997)
Annales de l'institut Fourier
We define Du Bois invariants for isolated singularities of complex spaces. We relate them to the Hodge numbers of the local and vanishing cohomology groups. Our main results express the Tjurina number of certain Gorenstein singularities in terms of Du Bois invariants and Hodge numbers of the link, and express the Hodge numbers of the Milnor fibre of certain three-dimensional complete intersections in similar terms. We also address the question of the semicontinuity of the Du Bois invariants under...
Gert-Martin Greuel (1980)
Mathematische Annalen
Hans-Jörg Reiffen, Heinz Trapp (1981)
Studia Mathematica
Hans-Jörg Reiffen (1982)
Mathematische Annalen
Jürgen Bingener, Hubert Flenner (1979)
Journal für die reine und angewandte Mathematik
G. Müller (1982)
Mathematische Annalen
Joël Briançon, J.P.G. Henry (1980)
Bulletin de la Société Mathématique de France
Max Benson, Stephen S.-T. Yau (1990)
Mathematische Annalen
Françoise Geandier (1991)
Compositio Mathematica
J. Briançon (1997)
Annales scientifiques de l'École Normale Supérieure
Ben Lichtin (1981)
Inventiones mathematicae
Pierrette Cassou-Noguès (1987)
Compositio Mathematica
Didier D'Acunto, Krzysztof Kurdyka (2005)
Annales Polonici Mathematici
Let f: ℝⁿ → ℝ be a polynomial function of degree d with f(0) = 0 and ∇f(0) = 0. Łojasiewicz’s gradient inequality states that there exist C > 0 and ϱ ∈ (0,1) such that in a neighbourhood of the origin. We prove that the smallest such exponent ϱ is not greater than with .
Morihiko Saito (1988)
Mathematische Annalen
D. Barlet (1985)
Inventiones mathematicae
Francois Loeser (1984)
Commentarii mathematici Helvetici
Dominique Manchon (1999)
Colloquium Mathematicae
We define the wave front set of a distribution vector of a unitary representation in terms of pseudo-differential-like operators [M2] for any real Lie group G. This refines the notion of wave front set of a representation introduced by R. Howe [Hw]. We give as an application a necessary condition so that a distribution vector remains a distribution vector for the restriction of the representation to a closed subgroup H, and we give a propagation of singularities theorem for distribution vectors.