Sur quelques aspects de la géométrie de l'espace des arcs tracés sur un espace analytique
| dc.creator | Hickel, Michel | |
| dc.date | 2004-05-24 | |
| dc.date.accessioned | 2026-07-07T05:08:31Z | |
| dc.date.available | 2026-07-07T05:08:31Z | |
| dc.description | 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. | |
| dc.description | 45 pages, french | |
| dc.identifier | https://arxiv.org/abs/math/0405453 | |
| dc.identifier | http://arxiv.org/abs/math/0405453 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/71297 | |
| dc.subject | Algebraic Geometry | |
| dc.subject | Category Theory | |
| dc.subject | 14B05; 32S05; 32S99 | |
| dc.title | Sur quelques aspects de la géométrie de l'espace des arcs tracés sur un espace analytique | |
| dc.type | text |