Sur quelques aspects de la géométrie de l'espace des arcs tracés sur un espace analytique

Michel Hickel

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arXiv · math/0405453

Sur quelques aspects de la géométrie de l'espace des arcs tracés sur un espace analytique

Michel Hickel

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Abstract

Let $(X,x)$ be a germ of real or complex analytic space and $\mathcal{A}_{(X,x)}$ the space of germs of arcs on $(X,x)$. Let us consider $F_{x}: (X,x) \to (Y,y)$ a germ of a morphism and denote by $\mathcal{F}_{x}: \mathcal{A}_{(X,x)} \to \mathcal{A}_{(Y,y)}$ the induced morphism at the level of arcs. In this paper, we try to emphasize the analogies between the metric or local topological properties of $F_{x}$ and those of $\mathcal{F}_{x}$. We then define the notions of Nash sequence of multiplicities, Nash sequence of Hilbert-Samuel functions and Nash sequence of diagram of initial exponents of $X$ along an arc $ϕ$, and study some of their basic properties. Some elementary connections between these notions and motivic integration theory are also provided.

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Michel Hickel. 2004-05-24. Sur quelques aspects de la géométrie de l'espace des arcs tracés sur un espace analytique. https://arxiv.org/abs/math/0405453

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