Blow-analytic equivalence of two variable real analytic function germs
نویسندگان
چکیده
منابع مشابه
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...
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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...
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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 ...
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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 ...
متن کاملMotivic-type Invariants of Blow-analytic Equivalence
To a given analytic function germ f : (R, 0) → (R, 0), we associate zeta functions Zf,+, Zf,− ∈ Z[[T ]], defined analogously to the motivic zeta functions of Denef and Loeser. We show that our zeta functions are rational and that they are invariants of the blow-analytic equivalence in the sense of Kuo. Then we use them together with the Fukui invariant to classify the blow-analytic equivalence ...
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ژورنال
عنوان ژورنال: Journal of Algebraic Geometry
سال: 2010
ISSN: 1056-3911,1534-7486
DOI: 10.1090/s1056-3911-09-00527-x