On the space of curves through a singularity. (Sur l’espace des courbes tracées sur une singularité.) (French) Zbl 0862.14003

Campillo López, Antonio (ed.) et al., Algebraic geometry and singularities. Proceedings of the 3rd international conference on algebraic geometry held at La Rábida, Spain, December 9-14, 1991. Basel: Birkhäuser. Prog. Math. 134, 9-32 (1996).
The paper is devoted to present recent developments on the study and classification of the arcs of a curve traced on a singular germ of an algebraic variety \(V\). There are presented computations of the spaces of jets of arcs of the curve using Artin’s theorem and they are applied to characterize the existence of smooth arcs traced on \(V\). Also some advances on the Nash problem, about relating the families of arcs and the desingularization of \(V\), are reported.
For the entire collection see [Zbl 0832.00033].


14B05 Singularities in algebraic geometry
14H10 Families, moduli of curves (algebraic)