The index of a holymorphic flow with an isolated singularity.
Displaying 161 – 180 of 195
The index of a vector field tangent to a hypersurface and the signature of the relative jacobian determinant
Xavier Gómez-Mont, Pavao Mardešić (1997)
Annales de l'institut Fourier
Given a real analytic vector field tangent to a hypersurface with an algebraically isolated singularity we introduce a relative Jacobian determinant in the finite dimensional algebra associated with the singularity of the vector field on . We show that the relative Jacobian generates a 1-dimensional non-zero minimal ideal. With its help we introduce a non-degenerate bilinear pairing, and its signature measures the size of this point with sign. The signature satisfies a law of conservation of...
The index of analytic vector fields and Newton polyhedra
Carles Bivià-Ausina (2003)
Fundamenta Mathematicae
We prove that if f:(ℝⁿ,0) → (ℝⁿ,0) is an analytic map germ such that and f satisfies a certain non-degeneracy condition with respect to a Newton polyhedron Γ₊ ⊆ ℝⁿ, then the index of f only depends on the principal parts of f with respect to the compact faces of Γ₊. In particular, we obtain a known result on the index of semi-weighted-homogeneous map germs. We also discuss non-degenerate vector fields in the sense of Khovanskiĭand special applications of our results to planar analytic vector fields....
The infinitesimal M. Noether theorem for singularities
Hubert Flenner (1986)
Compositio Mathematica
The jump of the Milnor number in the X 9 singularity class
Szymon Brzostowski, Tadeusz Krasiński (2014)
Open Mathematics
The jump of the Milnor number of an isolated singularity f 0 is the minimal non-zero difference between the Milnor numbers of f 0 and one of its deformations (f s). We prove that for the singularities in the X 9 singularity class their jumps are equal to 2.
The Lê varieties, I.
D.B. Massey (1990)
Inventiones mathematicae
The Le varieties, II.
David B. Massey (1991)
Inventiones mathematicae
The Le-Ramanujam Problem for Hypersurfaces with One-Dimensional Singular Sets.
David B. Massey (1988)
Mathematische Annalen
The Łojasiewicz exponent of an analytic mapping of two complex variables at an isolated zero
Jacek Chadzyński, Tadeusz Krasiński (1988)
Banach Center Publications
The Łojasiewicz gradient inequality in a neighbourhood of the fibre
Janusz Gwoździewicz, Stanisław Spodzieja (2005)
Annales Polonici Mathematici
Some estimates of the Łojasiewicz gradient exponent at infinity near any fibre of a polynomial in two variables are given. An important point in the proofs is a new Charzyński-Kozłowski-Smale estimate of critical values of a polynomial in one variable.
The Łojasiewicz numbers and plane curve singularities
Evelia García Barroso, Tadeusz Krasiński, Arkadiusz Płoski (2005)
Annales Polonici Mathematici
For every holomorphic function in two complex variables with an isolated critical point at the origin we consider the Łojasiewicz exponent ₀(f) defined to be the smallest θ > 0 such that near 0 ∈ ℂ² for some c > 0. We investigate the set of all numbers ₀(f) where f runs over all holomorphic functions with an isolated critical point at 0 ∈ ℂ².
The Monodromy Groups of Critical Points of Functions II.
S.V. Chmutov (1983)
Inventiones mathematicae
The nilpotent part and distinguished form of resonant vector fields or diffeomorphisms
J. Ecalle, D. Schlomiuk (1993)
Annales de l'institut Fourier
The rational homotopy of Thom spaces and the smoothing of isolated singularities
Stefan Papadima (1985)
Annales de l'institut Fourier
Rational homotopy methods are used for studying the problem of the topological smoothing of complex algebraic isolated singularities. It is shown that one may always find a suitable covering which is smoothable. The problem of the topological smoothing (including the complex normal structure) for conical singularities is considered in the sequel. A connection is established between the existence of certain relations between the normal Chern degrees of a smooth projective variety and the question...
The Seiberg–Witten invariants of negative definite plumbed 3-manifolds
András Némethi (2011)
Journal of the European Mathematical Society
Assume that is a connected negative definite plumbing graph, and that the associated plumbed 3-manifold is a rational homology sphere. We provide two new combinatorial formulae for the Seiberg–Witten invariant of . The first one is the constant term of a ‘multivariable Hilbert polynomial’, it reflects in a conceptual way the structure of the graph , and emphasizes the subtle parallelism between these topological invariants and the analytic invariants of normal surface singularities. The second...
The topology of holomorphic flows with singularity
Cesar Camacho, Nicolaas H. Kuiper, Jacob Palis (1978)
Publications Mathématiques de l'IHÉS
Topological aspects of deformations of singularities.
Mond, David (2006)
Revista Colombiana de Matemáticas
Topological K-equivalence of analytic function-germs
Sérgio Alvarez, Lev Birbrair, João Costa, Alexandre Fernandes (2010)
Open Mathematics
We study the topological K-equivalence of function-germs (ℝn, 0) → (ℝ, 0). We present some special classes of piece-wise linear functions and prove that they are normal forms for equivalence classes with respect to topological K-equivalence for definable functions-germs. For the case n = 2 we present polynomial models for analytic function-germs.
Topologie comparée d'une courbe polaire et de sa courbe descriminante.
Hélène Maugendre (1999)
Revista Matemática Complutense
Let f be an analytic function germ at 0 in C2. We compare the topological complexity of the discriminant curve of f to the one of its polar curve.
Torelli theorems for singularieties (Erratum).
Yakov Karpishpan (1992)
Inventiones mathematicae