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Melle Hernández, Alejandro and Torrelli , Tristan and Veys, Willen (2010) Monodromy Jordan blocks, bfunctions and poles of Zeta functions for germs of plane curves. Journal of Algebra, 324 (6). 1364 1382. ISSN 00218693

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Official URL: http://www.sciencedirect.com/science/journal/00218693
Abstract
We study the poles of several local zeta functions: the Igusa, topological and motivic zeta function associated to a germ of a holomorphic function in two variables. It was known that there is at most one double pole for (any of) these zeta functions which is then given by the log canonical threshold of the function at the singular point. If the germ is reduced Loeser showed that such a double pole always induces a monodromy eigenvalue with a Jordan block of size 2. Here we settle the nonreduced situation, describing precisely in which case such a Jordan block of maximal size 2 occurs. We also provide detailed information about the BernsteinSato polynomial in the relevant nonreduced situation, confirming a conjecture of Igusa, Denef and Loeser.
Item Type:  Article 

Uncontrolled Keywords:  Igusa and topological zeta function; BernsteinSato polynomial; Monodromy; Log canonical threshold; Plane curve singularities 
Subjects:  Sciences > Mathematics > Algebraic geometry 
ID Code:  13914 
Deposited On:  18 Nov 2011 08:27 
Last Modified:  06 Feb 2014 09:55 
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