The motivic zeta function and its smallest poles

Details The motivic zeta function and its smallest poles The motivic zeta function and its smallest poles

2007-10-31

arxiv.org/abs/0710.5911v1

Journal of Algebra 317 (2007) 851-866

Mathematics

Algebraic Geometry

Scientific paper

10.1016/j.jalgebra.2007.05.012

Let f be a regular function on a nonsingular complex algebraic variety of dimension d. We prove a formula for the motivic zeta function of f in terms of an embedded resolution. This formula is over the Grothendieck ring itself, and specializes to the formula of Denef and Loeser over a certain localization. We also show that the space of n-jets satisfying f=0 can be partitioned into locally closed subsets which are isomorphic to a cartesian product of some variety with an affine space of dimension the round up of dn/2. Finally, we look at the consequences for the poles of the motivic zeta function.

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