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Using the theory of jet schemes, we give a new approach to the description ofa minimal generating sequence of a divisorial valuations on $\textbf{A}^2.$ Forthis purpose, we show how one can recover the approximate roots of ananalytically irreducible plane curve from the equations of its jet schemes. Asan application, for a given divisorial valuation $v$ centered at the origin of$\textbf{A}^2,$ we construct an algebraic embedding$\textbf{A}^2\hookrightarrow \textbf{A}^N,N\geq 2$ such that $v$ is the traceof a monomial valuation on $\textbf{A}^N.$ We explain how results in thisdirection give a constructive approach to a conjecture of Teissier onresolution of singularities by one toric morphism.

Jet schemes and generating sequences of divisorial valuations in dimension two