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

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

2004-05-24

arxiv.org/abs/math/0405453v1

Mathematics

Algebraic Geometry

45 pages, french

Scientific paper

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 $\phi$, and study some of their basic properties. Some elementary connections between these notions and motivic integration theory are also provided.

Affiliated with

Also associated with

No associations

Rating

Sur quelques aspects de la géométrie de l'espace des arcs tracés sur un espace analytique does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Sur quelques aspects de la géométrie de l'espace des arcs tracés sur un espace analytique, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Sur quelques aspects de la géométrie de l'espace des arcs tracés sur un espace analytique will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-712102