Invariants of the graded algebras associated to divisorial valuations dominating a rational surface singularity

  • Vincent Cossart

    Université de Versailles Saint-Quentin, Versailles, France
  • Olivier Piltant

    Université de Versailles Saint-Quentin, Versailles, France
  • Ana J. Reguera

    Universidad de Valladolid, Spain
Invariants of the graded algebras associated to divisorial valuations dominating a rational surface singularity cover
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Abstract

Let (R,M)(R,M) be a rational surface singularity and νE\nu_E be a prime divisor of the second kind for RR. Then grνERgr_{\nu_E} R is finitely generated over R/MR/M. We recover information about the dual graph of the minimal resolution X~\widetilde X of Spec R\text{Spec } R from the set of all grνERgr_{\nu_E} R. In particular we characterize those graded algebras corresponding to the exceptional curves in X~\widetilde X.