Results 121 to 130 of about 2,631,518 (164)

Milnor Number and Milnor Classes

2009
Both Schwartz–MacPherson and Fulton–Johnson classes generalize Chern classes to the case of singular varieties. It is known that for local complete intersections with isolated singularities, the 0-degree SM and FJ classes differ by the local Milnor numbers [149] and all other classes coincide [155].
Jean-Paul Brasselet, José Seade, Tatsuo Suwa   +2 more
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The spectral genus of an isolated hypersurface singularity and its relation to the Milnor number and analytic torsion

Documenta Mathematica
In this paper, we introduce the notion of spectral genus \tilde{p}_{g} of a germ of an isolated hypersurface singularity (\mathbb{C}^{n+1},0)\to (\mathbb{C},0) , defined as a sum of small exponents of monodromy eigenvalues.
D. Eriksson, Gerard Freixas i Montplet
semanticscholar   +1 more source

Milnor numbers of nonisolated saito singularities

Functional Analysis and Its Applications, 1987
It is shown that Milnor numbers of a quasihomogeneous Saito singularity can be calculated by investigating the cohomology groups of a complex on certain affine space.
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On Milnor's triple linking number

Comptes Rendus de l'Académie des Sciences - Series I - Mathematics, 1997
Summary: We define an operation of summation of 3 knots along a \(Y\)-graph, similar to the band sum of 2 components. Starting from the second degree Vassiliev knot invariant, we obtain, by means of \(Y\)-summation, Milnor's triple linking number \(\overline \mu_{123}\).
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Equivariant Milnor Numbers and Invariant Morse Approximations

Journal of the London Mathematical Society, 1985
Let G be a finite group, V an orthogonal complex representation of G and f: (V,0)\(\to {\mathbb{C}}\) the germ of a G-invariant holomorphic function with an isolated critical point. This paper proves that there is a deformation of a representative of f, through invariant functions, in which the generic fibre has only non-degenerate (or Morse) critical ...
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Bounding Poincaré‐Hopf indices and Milnor numbers

Mathematische Nachrichten, 2005
AbstractWe use Mather's finite determinacy theory and Baum‐Bott's theorem to give sharp bounds for the Poincaré‐Hopf index of a germ of homolorphic vector field with an isolated zero. (© 2005 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)
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A New Deterministic Method for Computing Milnor Number of an ICIS

Computer Algebra in Scientific Computing, 2021
S. Tajima, Katsusuke Nabeshima
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The Invariance of Milnor's Number Implies Topological Triviality

American Journal of Mathematics, 1977
THEOREM. Let F(z, t) be a polynomial in z = (z0, ... , zn) with coefficients which are smooth complex valued functions of t E RP such that F(O t) = 0, and for each t E RP, the polynomials aF/azi(z, t) in z have an isolated zero at 0. Assume moreover that the Milnor numbers ,t are independent of t, and that n # 2.
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On Milnor–Orlik’s theorem and admissible simultaneous good resolutions

Annales Polonici Mathematici
Let f be a (possibly Newton degenerate) weighted homogeneous polynomial defining an isolated surface singularity at the origin of C3, and let {fs} be a generic deformation of its coefficients such that fs is Newton non-degenerate for s/=0.
C. Eyral, M. Oka
semanticscholar   +1 more source

On the Milnor Number of an Equivariant Singularity

Mathematical Notes, 2002
Let \(f : (\mathbb{C}^n,0) \to (\mathbb{C},0)\) be a holomorphic germ being invariant under a non-trivial action of the group \(\mathbb{Z}/p\), \(p\) prime, with isolated critical point at \(0\) such that the 2--jet of \(f\) is \(0\). It is proved that the Milnor number \(\mu(f) \geq p - 1\).
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