Symmetries of some motivic integrals

Details Symmetries of some motivic integrals Symmetries of some motivic integrals

2008-04-05

arxiv.org/abs/0804.0844v1

Mathematics

Algebraic Geometry

12 pages

Scientific paper

We give an explicit formula for the motivic integrals related to the Milnor number over spaces of parametrised arcs on the plane with fixed tangency orders with the axis. These integrals are rational functions of the parameters and the class of the affine line. Using a set of natural recurrence relations between them, we prove an unexpected invariance property with respect to the simultaneous inversion of the parameters and the class of the affine line. We also discuss a generalization of this system of recurrence relations whose solutions are also symmetric and satisfy additional differential equations.

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