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Remarks on the generalized index of an analytic improper intersection

Krzysztof Jan Nowak (2003)

Annales Polonici Mathematici

This article continues the investigation of the analytic intersection algorithm from the perspective of deformation to the normal cone, carried out in the previous papers of the author [7, 8, 9]. The main theorem asserts that, given an analytic set V and a linear subspace S, every collection of hyperplanes, admissible with respect to an algebraic bicone B, realizes the generalized intersection index of V and S. This result is important because the conditions for a collection of hyperplanes to be...

Representation theory for log-canonical surface singularities

Trond Stølen Gustavsen, Runar Ile (2010)

Annales de l’institut Fourier

We consider the representation theory for a class of log-canonical surface singularities in the sense of reflexive (or equivalently maximal Cohen-Macaulay) modules and in the sense of finite dimensional representations of the local fundamental group. A detailed classification and enumeration of the indecomposable reflexive modules is given, and we prove that any reflexive module admits an integrable connection and hence is induced from a finite dimensional representation of the local fundamental...

Resultant and the Łojasiewicz exponent

J. Chądzyński, T. Krasiński (1995)

Annales Polonici Mathematici

An effective formula for the Łojasiewicz exponent of a polynomial mapping of ℂ² into ℂ² at an isolated zero in terms of the resultant of its components is given.

Réversibilité et classification des centres nilpotents

Michel Berthier, Robert Moussu (1994)

Annales de l'institut Fourier

Nous considérons un germe ω de 1-forme analytique dans ℝ 2 , 0 dont le 1-jet est y d y . Nous montrons que si l’équation ω = 0 définit un centre (i.e toutes les courbes solutions sont des cycles) il existe une involution analytique de ℝ 2 , 0 préservant le portrait de phase du système. Géométriquement ceci signifie que les centres analytiques nilpotents sont obtenus par image réciproque par des applications pli. Un théorème de conjugaison équivariante permet d’obtenir une classification complète de ces centres.

Rigidity of CR morphisms between compact strongly pseudoconvex CR manifolds

Stephen S.-T. Yau (2011)

Journal of the European Mathematical Society

Let X 1 and X 2 be two compact strongly pseudoconvex CR manifolds of dimension 2 n - 1 ≥ 5 which bound complex varieties V 1 and V 2 with only isolated normal singularities in ℂ N 1 and ℂ N 2 respectively. Let S 1 and S 2 be the singular sets of V 1 and V 2 respectively and S 2 is nonempty. If 2 n - N 2 - 1 ≥ 1 and the cardinality of S 1 is less than 2 times the cardinality of S 2 , then we prove that any non-constant CR morphism from X 1 to X 2 is necessarily a CR biholomorphism. On the other hand, let X be a compact strongly pseudoconvex CR manifold of...

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