Results 11 to 20 of about 1,001 (184)
On Sextic Curves with Big Milnor Number [PDF]
, 2002 In this work we present an exhaustive description, up to projective isomorphism, of all irreducible sextic curves in ℙ2 having a singular point of type , A n ,n⩾15 n ≥ 15, only rational singularities and global Milnor number at least 18. Moreover, we develop a method for an explicit construction of sextic curves with at least eight — possibly ...
Artal Bartolo, Enrique +2 more
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Milnor Number Equals Tjurina Number for Functions on Space Curves [PDF]
Journal of the London Mathematical Society, 2001 In many situations in complex geometry one can define a Milnor number, \(\mu\), that describes the rank of some vanishing homology, and a Tjurina number, \(\tau\), the dimension of the base of a semi-universal deformation. For example, for a hypersurface singularity \(X=V(f)\), one has \[ \mu=\dim {\mathcal O}/J_f,\quad \tau=\dim {\mathcal O}/(f,J_f), \
Mond, D. (David), Straten, Duco van
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A formula for the Milnor Number [PDF]
, 1995 We give a formula for the Milnor number of a germ (X,0) subset of (C-n+1,0) defined by f=0, f=f(d)+f(d+k)+...epsilon C {x(0),...,x(n)}, and such that Sing(D) boolean AND Z (f(d+k)) = circle divide, where D=Z (f(d)) subset of P-C(n). We prove that the topological type of (X,0) is determined by the d+k-jet of f.
Melle Hernández, Alejandro +1 more
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Milnor Number and Chern Classes for Singular Varieties: An Introduction
, 2022 We survey how the Milnor number of complex map-germs with an isolated critical point relates to various indices of vector fields on singular varieties, and the way how this number extends via the theory of Chern classes of singular varieties, to the concept of Milnor classes of varieties with arbitrary singular set in complex manifolds.
Callejas-Bedregal, Roberto +2 more
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Milnor numbers for surface singularities [PDF]
Israel Journal of Mathematics, 2000 An additive formula for the Milnor number of an isolated complex hypersurface singularity is shown. We apply this formula for studying surface singularities. Durfee's conjecture is proved for any absolutely isolated surface and a generalization of Yomdin singularities is given.
Melle Hernández, Alejandro
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The Milnor Number of Plane Branches with Tame Semigroups of Values
Bulletin of the Brazilian Mathematical Society, New Series, 2018 The Milnor number of an isolated hypersurface singularity, defined as the codimension $μ(f)$ of the ideal generated by the partial derivatives of a power series $f$ that represents locally the hypersurface, is an important topological invariant of the singularity over the complex numbers.
A. Hefez +2 more
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Note on Milnor numbers of irreducible germs
, 2023 Let $(\bf {V,0})\subset (\mathbb{C}^n,0)$ be a germ of a complex hypersurface and let $f: (\mathbb{C}^n,0)\to(\mathbb{C}^n,0)$ be a germ of a finite holomorphic mapping. If germs $(\bf {V,0})$ and ${\bf W}:=(F^{-1}(\bf{ V})),0)$ are irreducible and with isolated singularities, then $$μ(F^{-1}(\bf{ V}))\ge μ(\bf {V}),$$ where $μ$ denotes the Milnor ...
Jelonek, Zbigniew
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TJURINA AND MILNOR NUMBERS OF MATRIX SINGULARITIES [PDF]
Journal of the London Mathematical Society, 2005 LaTeX file; 23 pages; minor ...
Goryunov, Victor V., Mond, D. (David)
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Linking number and Milnor invariants
, 2021 14 pagesInternational audienceThis is a concise overview of the definitions and properties of the linking number and its higher-order generalization, Milnor ...
Meilhan, Jean-Baptiste
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Deformations of functions and F-manifolds [PDF]
, 2004 We study deformations of functions on isolated singularities. A unified proof of the equality of Milnor and Tjurina numbers for functions on isolated complete intersections singularities and space curves is given.
De Gregorio, Ignacio +1 more
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