Integration over spaces of non-parametrized arcs and motivic versions of the monodromy zeta function

Details Integration over spaces of non-parametrized arcs and motivic versions of the monodromy zeta function Integration over spaces of non-parametrized arcs and motivic versions of the monodromy zeta function

2004-07-12

arxiv.org/abs/math/0407201v1

Mathematics

Algebraic Geometry

Scientific paper

We elaborate notions of integration over the space of arcs factorized by the natural $C^*$-action and over the space of non-parametrized arcs (branches). There are offered two motivic versions of the zeta function of the classical monodromy transformation of a germ of an analytic function on a smooth space. We indicate a direct formula which connects the naive motivic zeta function of J. Denef and F. Loeser with the classical monodromy zeta function.

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