scholarly journals Local Łojasiewicz exponents, Milnor numbers and mixed multiplicities of ideals

2008 ◽  
Vol 262 (2) ◽  
pp. 389-409 ◽  
Author(s):  
Carles Bivià-Ausina
Keyword(s):  
Łojasiewicz Exponents ◽  
Milnor Numbers

scholarly journals Milnor numbers in deformations of homogeneous singularities

2021 ◽  
pp. 102973
Author(s):  
Szymon Brzostowski ◽  
Tadeusz Krasiński ◽  
Justyna Walewska
Keyword(s):  
Milnor Numbers

scholarly journals The jump of the Milnor number in the X 9 singularity class

2014 ◽  
Vol 12 (3) ◽  
Author(s):  
Szymon Brzostowski ◽  
Tadeusz Krasiński
Keyword(s):  
Milnor Number ◽  
Isolated Singularity ◽  
Milnor Numbers

AbstractThe jump of the Milnor number of an isolated singularity f 0 is the minimal non-zero difference between the Milnor numbers of f 0 and one of its deformations (f s). We prove that for the singularities in the X 9 singularity class their jumps are equal to 2.

Bounding Poincaré-Hopf indices and Milnor numbers

2005 ◽  
Vol 278 (6) ◽  
pp. 703-711 ◽  
Author(s):  
Marcio G. Soares
Keyword(s):  
Milnor Numbers

scholarly journals Terminal singularities, Milnor numbers, and matter in F-theory

2018 ◽  
Vol 123 ◽  
pp. 71-97 ◽  
Author(s):  
Philipp Arras ◽  
Antonella Grassi ◽  
Timo Weigand
Keyword(s):  
Milnor Numbers

scholarly journals Algorithms for residues and Lojasiewicz exponents

2000 ◽  
Vol 153 (1) ◽  
pp. 27-44 ◽  
Author(s):  
M. Elkadi ◽  
B. Mourrain
Keyword(s):  
Łojasiewicz Exponents

scholarly journals Topological invariants of plane curve singularities: Polar quotients and Łojasiewicz gradient exponents

2019 ◽  
Vol 30 (14) ◽  
pp. 1950073 ◽  
Author(s):  
Hong-Duc Nguyen ◽  
Tien-Son Phạm ◽  
Phi-Dũng Hoàng
Keyword(s):  
Complex Plane ◽  
Plane Curve ◽  
Complex Variables ◽  
Topological Invariant ◽  
Topological Invariants ◽  
Real Plane ◽  
Plane Curve Singularities ◽  
Łojasiewicz Exponents ◽  
Curve Singularities ◽  
Formula Computing

In this paper, we study polar quotients and Łojasiewicz exponents of plane curve singularities, which are not necessarily reduced. We first show that, for complex plane curve singularities, the set of polar quotients is a topological invariant. We next prove that the Łojasiewicz gradient exponent can be computed in terms of the polar quotients, and so it is also a topological invariant. For real plane curve singularities, we also give a formula computing the Łojasiewicz gradient exponent via real polar branches. As an application, we give effective estimates of the Łojasiewicz exponents in the gradient and classical inequalities of polynomials in two (real or complex) variables.

scholarly journals Jumps of Milnor Numbers of Brieskorn–Pham Singularities in Non-degenerate Families

2018 ◽  
Vol 73 (3) ◽  
Author(s):  
Tadeusz Krasiński ◽  
Justyna Walewska
Keyword(s):  
Milnor Numbers
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