Deformations of arcs and comparison of formal neighborhoods for a curve singularity
Résumé
Let $ \cC $ be an algebraic curve and $c$ be an analyticallyirreducible singular point of $\cC$. The set $\arc(\cC)^c$ of arcs withorigin $c$ is an irreducible closed subset of the space of arcs on$\cC$. We obtain a presentation of the formal neighborhood of thegeneric point of this set which can be interpreted in terms ofdeformations of the generic arc defined by this point. This allowsus to deduce a strong connection between the aforementioned formalneighborhood and the formal neighborhood in the arc space of anyprimitive parametrization of the singularity $c$. This may beinterpreted as the fact that analytically along $\arc(\cC)^c$ thearc space is a product of a finite dimensional singularity and aninfinite dimensional affine space.
Domaines
Géométrie algébrique [math.AG]
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