Generating sequences and Poincar\'e series for a finite set of plane divisorial valuations

@inproceedings{Delgado2008GeneratingSA,
  title={Generating sequences and Poincar\'e series for a finite set of plane divisorial valuations},
  author={Fabrizio Delgado and Carlos Galindo and Alejandro N'unez},
  year={2008}
}
Let $V$ be a finite set of divisorial valuations centered at a 2-dimensional regular local ring $R$. In this paper we study its structure by means of the semigroup of values, $S_V$, and the multi-index graded algebra defined by $V$, $\gr_V R$. We prove that $S_V$ is finitely generated and we compute its minimal set of generators following the study of reduced curve singularities. Moreover, we prove a unique decomposition theorem for the elements of the semigroup. The comparison between… CONTINUE READING
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