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

Sabir M. Gusein-Zade·Ignacio Luengo·Alejandro Melle-Hernandez
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Abstract

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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Sabir M. Gusein-Zade, Ignacio Luengo, Alejandro Melle-Hernandez. 2004-07-12. Integration over spaces of non-parametrized arcs and motivic versions of the monodromy zeta function. https://arxiv.org/abs/math/0407201

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