Results 41 to 50 of about 2,631,518 (164)
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
openaire +2 more sources
Terminal singularities, Milnor numbers, and matter in F-theory [PDF]
Journal of Geometry and Physics, 2018 47 pages, 6 figures, 12 ...
Arras, Philipp +2 more
openaire +4 more sources
Invariants of Topological Relative Right Equivalences
, 2012 The constancy of the Milnor number has several characterizations which were summarized by Greuel in 1986. This paper presents a study of these characterizations in the case of families of functions with isolated singularities defined on an analytic ...
Ahmed, Imran +2 more
core +1 more source
The complex gradient inequality with parameter [PDF]
, 2014 We prove that given a holomorphic family of holomorphic functions with isolated singularities at zero and constant Milnor number, it is possible to obtain the gradient inequality with a uniform exponent.Comment: A remark was added at the end and some ...
Denkowski, Maciej P.
core
Milnor numbers, spanning trees, and the Alexander–Conway polynomial
Advances in Mathematics, 2003 We study relations between the Alexander-Conway polynomial $\nabla_L$ and Milnor higher linking numbers of links from the point of view of finite-type (Vassiliev) invariants. We give a formula for the first non-vanishing coefficient of $\nabla_L$ of an m-component link L all of whose Milnor numbers $ _{i_1... i_p}$ vanish for $p\le n$. We express this
Masbaum, Gregor, Vaintrob, Arkady
openaire +3 more sources
On Milnor and Tjurina Numbers of Foliations
Bulletin of the Brazilian Mathematical Society, New Series39 pages, 3 ...
Arturo Fernández-Pérez +2 more
openaire +3 more sources
On topological invariance of the milnor number mod 2
Topology, 1993 Let \(f=(f_ 1,\dots,f_ n)\): \((\mathbb{R}^ n,0)\to (\mathbb{R}^ p,0 ...
Dudziński, P. +3 more
openaire +2 more sources
The Milnor number of a hypersurface singularity in arbitrary characteristic
, 2015 The Milnor number of an isolated hypersurface singularity, defined as the codimension $\mu(f)$ of the ideal generated by the partial derivatives of a power series $f$ whose zeros represent locally the hypersurface, is an important topological invariant ...
Hefez, Abramo +2 more
core
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 ...
openaire +2 more sources
Milnor numbers and classes of local complete intersections
Proceedings of the Japan Academy, Series A, Mathematical Sciences, 1999 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Brasselet, Jean-Paul +3 more
openaire +3 more sources