Arc spaces, motivic measure and Lipschitz geometry of real algebraic sets View Full Text


Ontology type: schema:ScholarlyArticle     


Article Info

DATE

2019-02-01

AUTHORS

Jean-Baptiste Campesato, Toshizumi Fukui, Krzysztof Kurdyka, Adam Parusiński

ABSTRACT

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 variables 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. More... »

PAGES

1-41

Identifiers

URI

http://scigraph.springernature.com/pub.10.1007/s00208-019-01805-8

DOI

http://dx.doi.org/10.1007/s00208-019-01805-8

DIMENSIONS

https://app.dimensions.ai/details/publication/pub.1111838500


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