scholarly journals On the monodromy of a function germ defined on an arrangement of hyperplanes

1999 ◽  
Vol 22 (3) ◽  
pp. 438-445 ◽  
Author(s):  
Maria Ioachim Zaharia
Keyword(s):  
Function Germ ◽  
Arrangement Of Hyperplanes

Characterizations of Simple Isolated Line Singularities

1999 ◽  
Vol 42 (4) ◽  
pp. 499-506 ◽  
Author(s):  
Alexandru Zaharia
Keyword(s):  
Function Germ ◽  
Critical Set ◽  
Line Singularity ◽  
Line Singularities

AbstractA line singularity is a function germ with a smooth 1-dimensional critical set . An isolated line singularity is defined by the condition that for every x ≠ 0, the germ of f at (x, 0) is equivalent to . Simple isolated line singularities were classified by Dirk Siersma and are analogous of the famous A − D − E singularities. We give two new characterizations of simple isolated line singularities.

scholarly journals Mixed Bruce–Roberts numbers

2020 ◽  
Vol 63 (2) ◽  
pp. 456-474 ◽  
Author(s):  
Carles Bivià-Ausina ◽  
Maria Aparecida Soares Ruas
Keyword(s):  
Analytic Function ◽  
Function Germ ◽  
Analytic Variety ◽  
Fundamental Properties ◽  
Complex Analytic Variety

AbstractWe extend the notions of μ*-sequences and Tjurina numbers of functions to the framework of Bruce–Roberts numbers, that is, to pairs formed by the germ at 0 of a complex analytic variety X ⊆ ℂn and a finitely ${\mathcal R}(X)$-determined analytic function germ f : (ℂn, 0) → (ℂ, 0). We analyze some fundamental properties of these numbers.

scholarly journals Depth in an Arrangement of Hyperplanes

1999 ◽  
Vol 22 (2) ◽  
pp. 167-176 ◽  
Author(s):  
P. J. Rousseeuw ◽  
M. Hubert
Keyword(s):  
Arrangement Of Hyperplanes

scholarly journals The deligne complex of a real arrangement of hyperplanes

1993 ◽  
Vol 131 ◽  
pp. 39-65 ◽  
Author(s):  
Luis Paris
Keyword(s):  
Vector Space ◽  
Finite Family ◽  
Real Vector Space ◽  
Real Vector ◽  
Arrangement Of Hyperplanes

Let V be a real vector space. An arrangement of hyperplanes in V is a finite family of hyperplanes of V through the origin. We say that is essential if ∩H ∊H = {0}

NON-NEGATIVE DEFORMATIONS OF WEIGHTED HOMOGENEOUS SINGULARITIES

2017 ◽  
Vol 60 (1) ◽  
pp. 175-185 ◽  
Author(s):  
J. J. NUÑO-BALLESTEROS ◽  
B. ORÉFICE-OKAMOTO ◽  
J. N. TOMAZELLA
Keyword(s):  
Sufficient Conditions ◽  
Additional Term ◽  
Milnor Number ◽  
Curve Singularity ◽  
Hypersurface Singularity ◽  
Weighted Degree ◽  
Function Germ ◽  
Analytic Variety ◽  
Complex Analytic Variety ◽  
Necessary And Sufficient

AbstractWe consider a weighted homogeneous germ of complex analytic variety (X, 0) ⊂ (ℂn, 0) and a function germ f : (ℂn, 0) → (ℂ, 0). We derive necessary and sufficient conditions for some deformations to have non-negative degree (i.e., for any additional term in the deformation, the weighted degree is not smaller) in terms of an adapted version of the relative Milnor number. We study the cases where (X, 0) is an isolated hypersurface singularity and the invariant is the Bruce-Roberts number of f with respect to (X, 0), and where (X, 0) is an isolated complete intersection or a curve singularity and the invariant is the Milnor number of the germ f: (X, 0) → ℂ. In the last part, we give some formulas for the invariants in terms of the weights and the degrees of the polynomials.

scholarly journals Rich cells in an arrangement of hyperplanes

1995 ◽  
Vol 226-228 ◽  
pp. 567-575 ◽  
Author(s):  
I. Bárány ◽  
H. Bunting ◽  
D.G. Larman ◽  
J. Pach
Keyword(s):  
Arrangement Of Hyperplanes
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