Results 1 to 10 of about 8,612,691 (178)
The jump of the Milnor number in the X 9 singularity class [PDF]
Open Mathematics, 2014 Abstract 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).
Brzostowski Szymon, Krasiński Tadeusz
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Milnor numbers and Euler obstruction* [PDF]
Bulletin of the Brazilian Mathematical Society, 2005 We determine the relation between the local Euler obstruction $Eu_f$ of a holomorphic function $f$ and different generalizations of the Milnor number for functions on singular spaces.
Alberto Verjovsky +2 more
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Bulletin of the Brazilian Mathematical Society, 2007 6 pages, 1 figure, v2: references ...
Arnaud Bodin
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A generalization of the Milnor number
Mathematische Annalen, 1988 Let M be an n-dimensional connected complex manifold and v be a holomorphic section of a holomorphic line bundle L over M. Take a connected component Y of the zero set X of v and any holomorphic connection \(D=D'+{\bar \partial}\) on L. Then Y is a connected component of the zero set of D'v. Take a small neighbourhood U of Y.
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The Image Milnor Number And Excellent Unfoldings [PDF]
The Quarterly Journal of Mathematics, 2021 Abstract We show three basic properties of the image Milnor number µI(f) of a germ $f\colon(\mathbb{C}^{n},S)\rightarrow(\mathbb{C}^{n+1},0)$ with isolated instability. First, we show the conservation of the image Milnor number, from which one can deduce the upper semi-continuity and the topological invariance for families.
Conejero, R. Giménez +1 more
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TOPOLOGICAL INVARIANTS AND MILNOR FIBRE FOR \(\mathcal{A}\)-FINITE GERMS \(C^2\) to \(C^3\)
Tạp chí Khoa học Đại học Đà Lạt, 2022 This note is the observation that a simple combination of known results shows that the usual analytic invariants of a finitely determined multi-germ \(f : (C^2 , S) → (C^3 , 0) \)—namely, the image Milnor number , the number of cross-caps and triple ...
Javier Fernández De Bobadilla +2 more
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The Geometry of the Milnor Number [PDF]
, 2022 In the first part of this thesis we derive a volume-preserving normal form for function germs in n complex variables which are right equivalent to the product of all coordinates. In the second part of the thesis we discuss and prove special cases of a conjecture, called bifurcation formula, which gives a relation between the Milnor numbers in a pencil ...
Szawlowski, Adrian +4 more
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Limit spectral distribution for non-degenerate hypersurface singularities
Comptes Rendus. Mathématique, 2022 We establish Kyoji Saito’s continuous limit distribution for the spectrum of Newton non-degenerate hypersurface singularities. Investigating Saito’s notion of dominant value in the case of irreducible plane curve singularities, we find that the log ...
Almirón, Patricio, Schulze, Mathias
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On the indeterminacy of Milnor’s triple linking number [PDF]
Journal of Knot Theory and Its Ramifications, 2020 In the 1950s Milnor defined a family of higher-order invariants generalizing the linking number. Even the first of these new invariants, the triple linking number, has received fruitful study since its inception. In the case that a link [Formula: see text] has vanishing pairwise linking numbers, this triple linking number gives an integer-valued ...
Jonah Amundsen +2 more
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VARIATIONS OF MILNOR’S TRIPLE LINKING NUMBER
JP Journal of Geometry and Topology, 2022 Topological polymers have various topological types, and they are expressed by graphs. However, the Jones polynomial, we have a difficulty to compute it; computational time is growing exponentially with respect to the crossing number. The simplest Vassiliev invariant is the linking number and thus we will seek a next simple one is as the Milnor's ...
Intawong, Kamolphat, Ito, Noboru
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