Jet schemes and generating sequences of divisorial valuations in dimension two

  title={Jet schemes and generating sequences of divisorial valuations in dimension two},
  author={Hussein Mourtada},
  journal={arXiv: Algebraic Geometry},
  • H. Mourtada
  • Published 12 November 2015
  • Mathematics
  • arXiv: Algebraic Geometry
Using the theory of jet schemes, we give a new approach to the description of a minimal generating sequence of a divisorial valuations on $\textbf{A}^2.$ For this purpose, we show how one can recover the approximate roots of an analytically irreducible plane curve from the equations of its jet schemes. As an 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… Expand
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