On analytic function germs of two complex variables

Blow-analytic Equivalence of Two Variable Real Analytic Function Germs

Blow-analytic equivalence is a notion for real analytic function germs, introduced by Tzee-Char Kuo in order to develop the real analytic equisingularity theory. In this paper we give several complete characterisations of blow-analytic equivalence in the two dimensional case in terms of the minimal resolutions, the real tree model for the arrangement of Newton-Puiseux roots, and the cascade blo...

Equivalence Relations for Two Variable Real Analytic Function Germs

For two variable real analytic function germs we compare the blowanalytic equivalence in the sense of Kuo to the other natural equivalence relations. Our main theorem states that C equivalent germs are blow-analytically equivalent. This gives a negative answer to a conjecture of Kuo. In the proof we show that the Puiseux pairs of real Newton-Puiseux roots are preserved by the C equivalence of f...

A Criterion for the Topological Equivalence of Two Variable Complex Analytic Function Germs

We show that two analytic function germs (C, 0) → (C, 0) are topologically right equivalent if and only if there is a one-to-one correspondence between the irreducible components of their zero sets, that preserves the multiplicites of these components, their Puiseux pairs, and the intersection numbers of any pairs of distinct components. By Zariski [7] and Burau [1], the topological type of an ...

A Criterion for Topological Equivalence of Two Variable Complex Analytic Function Germs

We show that two analytic function germs (C, 0) → (C, 0) are topologically right equivalent if and only if there is a one-to-one correspondence between the irreducible components of their zero sets that preserves the multiplicites of these components, their Puiseux pairs, and the intersection numbers of any pairs of distinct components. By Zariski [10] and Burau [2], the topological type of an ...

On Humbert matrix function of two complex variables under differential operator