Germs of arcs on singular algebraic varieties and motivic integration
Algebraic Geometry
2009-10-31 v1
Abstract
We study the scheme of formal arcs on a singular algebraic variety and its images under truncations. We prove a rationality result for the Poincare series of these images which is an analogue of the rationality of the Poincare series associated to p-adic points on a p-adic variety. The main tools which are used are semi-algebraic geometry in spaces of power series and motivic integration (a notion introduced by M. Kontsevich). In particular we develop the theory of motivic integration for semi-algebraic sets of formal arcs on singular algebraic varieties, we prove a change of variable formula for birational morphisms and we prove a geometric analogue of a result of Oesterle.
Keywords
Cite
@article{arxiv.math/9803039,
title = {Germs of arcs on singular algebraic varieties and motivic integration},
author = {J. Denef and F. Loeser},
journal= {arXiv preprint arXiv:math/9803039},
year = {2009}
}
Comments
Revised Nov. 1997, to appear in Inventiones Mathematicae, 27 pages