RT Journal Article
T1 Monodromy Jordan blocks, b-functions and poles of Zeta functions for germs of plane curves
A1 Melle Hernández, Alejandro
A1 Torrelli, Tristan
A1 Veys, Willen
AB 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 non-reduced situation, describing precisely in which case such a Jordan block of maximal size 2 occurs. We also provide detailed information about the Bernstein-Sato polynomial in the relevant non-reduced situation, confirming a conjecture of Igusa, Denef and Loeser.
PB Academic Press
SN 0021-8693
YR 2010
FD 2010-09-15
LK https://hdl.handle.net/20.500.14352/42003
UL https://hdl.handle.net/20.500.14352/42003
LA eng
NO Spanish Contract
NO Fund of Scientific Research - Flanders
DS Docta Complutense
RD 23 may 2026