Coordinates at stable points of the space of arcs
Let \(X\) be a variety over a field \(k\) of characteristic 0 and let \(X_\infty\) be its space of arcs (see [\textit{J. F. Nash jun.}, Duke Math. J. 81, No. 1, 31--38 (1995; Zbl 0880.14010)]). Let \(P_E\) be the stable point of \(X_\infty\) defined by a divisorial valuation \(\nu_E\) on \(X\). The author investigates the analytic structure of the local ring \(\mathcal O_{X_\infty, P_E}\). In particular, she finds a suitable coordinate representation for the completion of this ring with respect to its maximal ideal, computes generators (a regular system of parameters) of the ring, its embedding dimension, and so on.
scientific article; zbMATH DE number 6807250
scientific article