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

Gusein-Zade, Sabir M.; Luengo, Ignacio; Melle-Hernandez, Alejandro

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

Authors

Gusein-Zade, Sabir M.

Luengo, Ignacio

Melle-Hernandez, Alejandro

Description

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.