Results 131 to 140 of about 21,780 (149)

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 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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The enhanced Milnor number in higher dimensions

1988
The "enhanced Milnor number" of a fibered link was introduced homotopy theoretically in [N-R I] . We recall its definition later. It lies in Z(~Z or Z(~(Z/2) according as the ambient dimension is 3 or greater than 3. Its first component is, up to sign, the usual Milnor number, which is the dimension of the Seifert form if the fibered link is simple. We
Walter D. Neumann, Lee Rudolph
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A hyperplane section theorem for Milnor numbers

Mathematische Annalen, 1997
We prove the following result. Theorem. Let \(R\) denote the power series ring \(\mathbb{C} [[X_1,X_2, \dots, X_n]]\) and \(f\in R\) any irreducible element. Assume that for any element \(h\in R\) which is a part of a minimal system of generators of the maximal ideal of \(R\) the ring \(R/(f,h)\) has an isolated singular point.
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On the quotient of Milnor and Tjurina numbers for two‐dimensional isolated hypersurface singularities

Mathematische Nachrichten, 2022
Patricio Almirón
exaly  

Newton polyhedron and Milnor numbers

Functional Analysis and Its Applications, 1975
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Singular Milnor numbers of non-isolated matrix singularities

2010
In this dissertation we obtain formulas to describe the local topology of certain non-isolated matrix singularities. We find free divisors in various vector spaces of matrices which include the hypersurface of singular matrices as a component, and use these to express the singular Milnor numbers of matrix singularities in terms of the codimensions of ...
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The Milnor-Palamodov Theorem for Functions on Isolated Hypersurface Singularities

Bulletin of the Brazilian Mathematical Society, 2020
Konstantinos Kourliouros
exaly  

The Milnor number and deformations of complex curve singularities

Inventiones Mathematicae, 1980
Gert-Martin Greuel
exaly  

Foliations on $$\mathbb {CP}^2$$ CP 2 of degree d with a singular point with Milnor number $$d^2+d+1$$ d 2 + d + 1

Revista Matematica Complutense, 2017
Claudia R Alcántara
exaly