Results 161 to 170 of about 1,001 (184)

A New Deterministic Method for Computing Milnor Number of an ICIS

2021
The Milnor number of an isolated complete intersection singularity (ICIS) is considered in the context of symbolic computation. Based on the classical Le-Greuel formula, a new method for computing Milnor numbers is introduced. Key ideas of our approach are the use of auxiliary indeterminates and the concept of local cohomology with coefficients in the ...
Shinichi 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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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 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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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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On the quotient of Milnor and Tjurina numbers for two‐dimensional isolated hypersurface singularities

Mathematische Nachrichten, 2022
Patricio Almirón
exaly  

The Kontsevich integral and Milnor’s invariants

Topology, 2000
Nathan Habegger
exaly  

Results on Milnor Fibrations for Mixed Polynomials with Non-isolated Singularities

Bulletin of the Brazilian Mathematical Society, 2020
R S Martins
exaly  

Characteristic cycles of perverse sheaves and Milnor fibers

Mathematische Zeitschrift, 2004
Philibert Nang
exaly  

Milnor-type theorems for left-invariant Riemannian metrics on Lie groups

Journal of the Mathematical Society of Japan, 2016
Takahiro Hashinaga, Hiroshi Tamaru
exaly