scholarly journals Modified Nash triviality theorem for a family of zero-sets of weighted homogeneous polynomial mappings

1997 ◽  
Vol 49 (3) ◽  
pp. 617-631 ◽  
Author(s):  
Satoshi KOIKE
Keyword(s):  
Homogeneous Polynomial ◽  
Zero Sets ◽  
Polynomial Mappings ◽  
Weighted Homogeneous Polynomial

scholarly journals Topological invariants of weighted homogeneous polynomials

1991 ◽  
Vol 33 (3) ◽  
pp. 241-245 ◽  
Author(s):  
Zbigniew Szafraniec
Keyword(s):  
Euler Characteristic ◽  
Homogeneous Polynomial ◽  
Topological Invariants ◽  
Homogeneous Polynomials ◽  
Weighted Homogeneous Polynomial

Let ℝn → ℝ be a weighted homogeneous polynomial such that df(0) = 0, L = {x ∈ Sn−1|f(x) = 0}, and let χ(L) be the Euler characteristic of L. The problem is how to calculate χ(L) in terms of f.

scholarly journals THE ŁOJASIEWICZ EXPONENT FOR WEIGHTED HOMOGENEOUS POLYNOMIAL WITH ISOLATED SINGULARITY

2016 ◽  
Vol 59 (2) ◽  
pp. 493-502
Author(s):  
OULD M. ABDERRAHMANE
Keyword(s):  
Explicit Formula ◽  
Homogeneous Polynomial ◽  
Isolated Singularity ◽  
Łojasiewicz Exponent ◽  
Lojasiewicz Exponent ◽  
Weighted Homogeneous Polynomial

AbstractThe purpose of this paper is to give an explicit formula of the Łojasiewicz exponent of an isolated weighted homogeneous singularity in terms of its weights.

scholarly journals Modified Nash triviality of a family of zero-sets of real polynomial mappings

1998 ◽  
Vol 48 (5) ◽  
pp. 1395-1440 ◽  
Author(s):  
Toshizumi Fukui ◽  
Satoshi Koike ◽  
Masahiro Shiota
Keyword(s):  
Real Polynomial ◽  
Zero Sets ◽  
Polynomial Mappings
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