Results 11 to 20 of about 2,631,518 (164)
A Lê-Greuel type formula for the image Milnor number [PDF]
Hokkaido Mathematical Journal, 2019 Accepted in Hokkaido Mathematical ...
J. J. NUÑO-BALLESTEROS +1 more
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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.
Adam Parusifiski
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A bound for the Milnor number of plane curve singularities [PDF]
Open Mathematics, 2014 Let f = 0 be a plane algebraic curve of degree d > 1 with an isolated singular point at 0 ∈ ℂ2. We show that the Milnor number μ0(f) is less than or equal to (d−1)2 − [d/2], unless f = 0 is a set of d concurrent lines passing through 0, and characterize ...
Płoski Arkadiusz
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Constant milnor number implies constant multiplicity for quasihomogeneous singularities
Manuscripta Mathematica, 1986 The author studies that the multiplicity does not change for certain topologically trivial deformations of an isolated hypersurface singularity. His work applies to all \(\mu\)-constant first order deformations and to all \(\mu\)-constant deformations of a quasihomogeneous singularity, i.e., an isolated hypersurface singularity with \({\mathbb{C ...
G. Greuel
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On the Milnor number of non‐isolated singularities of holomorphic foliations and its topological invariance [PDF]
Journal of Topology, 2021 We define the Milnor number of a one‐dimensional holomorphic foliation F$\mathcal {F}$ as the intersection number of two holomorphic sections with respect to a compact connected component C$C$ of its singular set.
A. Fern'andez-P'erez +2 more
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On deformation with constant Milnor number and Newton polyhedron [PDF]
, 2015 We show that every $$\mu $$μ-constant family of isolated hypersurface singularities satisfying a nondegeneracy condition in the sense of Kouchnirenko, is topologically trivial, also is equimultiple.
Ould M. Abderrahmane
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Milnor numbers in deformations of homogeneous singularities [PDF]
Bulletin des Sciences Mathématiques, 2021 Let f_0 be a plane curve singularity. We study the Minor numbers of singularities in deformations of f_0. We completely describe the set of these Milnor numbers for homogeneous singularities f_0 in the case of non-degenerate deformations and obtain some partial results on this set in the general case.
Brzostowski, Szymon +2 more
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Solvable Groups, Free Divisors and Nonisolated Matrix Singularities II: Vanishing Topology [PDF]
, 2013 In this paper we use the results from the first part to compute the vanishing topology for matrix singularities based on certain spaces of matrices. We place the variety of singular matrices in a geometric configuration of free divisors which are the ...
Brian Pike +16 more
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Image Milnor Number Formulas for Weighted-Homogeneous Map-Germs [PDF]
Results in Mathematics, 2021 We give formulas for the image Milnor number of a weighted-homogeneous map-germ $(\mathbb{C}^n,0)\to(\mathbb{C}^{n+1},0)$, for $n=4$ and $5$, in terms of weights and degrees. Our expressions are obtained by a purely interpolative method, applied to a result by Ohmoto. We use our approach to recover the formulas for $n=2$ and $3$ due to Mond and Ohmoto,
Irma Pallarés +1 more
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