Image Milnor Number Formulas for Weighted-Homogeneous Map-Germs

Milnor Number of Weighted-Lê–Yomdin Singularities

Weighted Homogeneous Map Germs of Corank One from C3 to C3 and Polar Multiplicities

For quasi-homogeneous and finitely determined corank one map germs f : (C, 0) → (C, 0) we obtain formulae in function of the degree and weight of f for invariantes on the stable types of f , as polar multiplicities, number of Milnor, number of Lê. We minimize also the number of invariantes for 7, to resolve the problem that decides the Whitney equisingularity of families of such maps germs. To ...

Homogeneous Polynomials with Isomorphic Milnor Algebras

In this note we recall first Mather’s Lemma 2.4 providing effective necessary and sufficient conditions for a connected submanifold to be contained in an orbit. In Theorem 3.2 we show that two homogeneous polynomials f and g having isomorphic Milnor algebras are right-equivalent. This is similar to the celebrated theorem by Mather and Yau [4], saying that the isolated hypersurface singularities...

Analytic surface germs with minimal Pythagoras number

We determine all complete intersection surface germs whose Pythagoras number is 2, and find they are all embedded in R and have the property that every positive semidefinite analytic function germ is a sum of squares of analytic function germs. In addition, we discuss completely these properties for mixed surface germs in R. Finally, we find in higher embedding dimension three different familie...

A Fatou Type Theorem for Complex Map Germs

In this paper we prove a Fatou type theorem for complex map germs. More precisely, we give (generic) conditions assuring the existence of parabolic curves for complex map germs tangent to the identity, in terms of existence of suitable formal separatrices. Such a map cannot have finite orbits.