On the smallest poles of topological zeta functions

Details On the smallest poles of topological zeta functions On the smallest poles of topological zeta functions

2003-05-16

arxiv.org/abs/math/0305235v1

Compositio Math. 140 (2004) 130-144

Mathematics

Algebraic Geometry

18 pages, to appear in Compositio Math

Scientific paper

We study the local topological zeta function associated to a complex function
that is holomorphic at the origin of C^2 (respectively C^3). We determine all
possible poles less than -1/2 (respectively -1). On C^2 our result is a
generalization of the fact that the log canonical threshold is never in
]5/6,1[. Similar statements are true for the motivic zeta function.

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