Results 31 to 40 of about 2,631,518 (164)
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.
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Tree invariants and Milnor linking numbers with indeterminacy [PDF]
Journal of Knot Theory and Its Ramifications, 2020 This paper concerns the tree invariants of string links, introduced by Kravchenko and Polyak, which are closely related to the classical Milnor linking numbers also known as [Formula: see text]-invariants. We prove that, analogously as for [Formula: see text]-invariants, certain residue classes of tree invariants yield link-homotopy invariants of ...
R. Komendarczyk, A. Michaelides
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Bulletin of the Brazilian Mathematical Society, New Series, 2007 6 pages, 1 figure, v2: references ...
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Prevalence of Milnor Attractors and Chaotic Itinerancy in 'High'-dimensional Dynamical Systems
, 2003 Dominance of Milnor attractors in high-dimensional dynamical systems is reviewed, with the use of globally coupled maps. From numerical simulations, the threshold number of degrees of freedom for such prevalence of Milnor attractors is suggested to be $5
Kaneko, Kunihiko
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Milnor number and Tjurina number of complete intersections
Mathematische Annalen, 1985 Let (X,x) be an isolated complete intersection singularity of dimension \(n\geq 2\). The main result of this note is a formula for the difference of the Milnor number \(\mu\) (X,x) and dim \(T^ 1_{X,x}\) (the dimension of the base of a miniversal deformation of (X,x)). It is of the form: \(\mu(X,x)-\dim T^ 1_{X,x}=\sum^{n-1}_{p=0}h^{p,0}(X,x)+a_ 1+a_ 2+
Looijenga, Eduard, Steenbrink, Joseph
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Codimension Two Determinantal Varieties with Isolated Singularities [PDF]
, 2011 We study codimension two determinantal varieties with isolated singularities. These singularities admit a unique smoothing, thus we can define their Milnor number as the middle Betti number of their generic fiber.
Maria Aparecida +2 more
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Hodge theory of abelian covers of algebraic varieties
Forum of Mathematics, SigmaMotivated by classical Alexander invariants of affine hypersurface complements, we endow certain finite dimensional quotients of the homology of abelian covers of complex algebraic varieties with a canonical and functorial mixed Hodge structure (MHS ...
Eva Elduque, Moisés Herradón Cueto
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Milnor Invariants and Twisted Whitney Towers
, 2014 This paper describes the relationship between the first non-vanishing Milnor invariants of a classical link and the intersection invariant of a twisted Whitney tower.
Conant, James +2 more
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Finite Jumps in Milnor Number Imply Vanishing Folds [PDF]
Proceedings of the American Mathematical Society, 1983 Let { X t } \left \{ {{X_t}} \right \} be a family of isolated hypersurface singularities in which the Milnor number is not constant. It is proved that there must be a vanishing fold centered at any t =
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