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Arc spaces, motivic measure and Lipschitz geometry of real algebraic sets. (arXiv:1807.05160v1 [math.AG])
来源于:arXiv
We investigate connections between Lipschitz geometry of real algebraic
varieties and properties of their arc spaces. For this purpose we develop
motivic integration in the real algebraic set-up. We construct a motivic
measure on the space of real analytic arcs. We use this measure to define a
real motivic integral which admits a change of variable formula not only for
the birational but also for generically one-to-one Nash maps.
As a consequence we obtain an inverse mapping theorem which holds for
continuous rational maps and, more generally, for generically arc-analytic
maps. These maps appeared recently in the classification of singularities of
real analytic function germs.
Finally, as an application, we characterize in terms of the motivic measure,
germs of arc-analytic homeomorphism between real algebraic varieties which are
bi-Lipschitz for the inner metric. 查看全文>>