GTA Seminar: Parusinski -- Introduction to Abhyankar-Jung Theorem

Speaker: Prof. Adam Parusinski (Nice)

http://math.unice.fr/~parus/

Time: Thursday, August 1, 12NOON--1PM

Room: Carslaw 707A

Lunch: after the talk, at Law Annex Cafe. 

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Title: Introduction to Abhyankar-Jung Theorem

Abstract: Abhyankar-Jung Theorem is a multivariable generalization of 
Newton-Puiseux Theorem. It says that the roots of a polynomial 

$P(Z) = Z^d+a_1 (X) Z^{d-1}+ . . . +a_d(X)$, 

where $a_i (X)$ are complex analytic function germs of many complex 
variables $X=(X_1, …,X_n)$, are convergent fractional (i.e. with 
positive rational exponents) power series, provided the discriminant 
of $P$ is a monomial in $X$ times an analytic unit. A similar 
statement holds for formal power series over an algebraically closed 
field $K$ of characteristic zero.

In this talk we give also a constructive proof of the latter statement
by completing an old proof of Luengo. Our method can be applied to 
any Henselian local subring of $K[[X]]$ in particular to the 
quasi-analytic functions. 

(This is joint work with Guillaume Rond from Marseille.)
 
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Seminar website:

http://www.maths.usyd.edu.au/u/SemConf/Geometry/