… The goal of this article, following the spirit in [6], is to show that there is a minimal toric
embedded resolution when X is a surface with rational singularities of multiplicity 3 (RTP-singularities
for short) and to provide an algorithm to build it. The complete list of the minimal abstract
resolution graphs of RTP-singularities is presented in [5] where the author gives a
characterization of rational singularities via their minimal abstract resolution graphs and
proved that the embedding dimension for a rational singularity equals ”multiplicity + 1”. The …

… Minimality of a toric embedded resolution of singularities after Bouvier-Gonzalez-Sprinberg …
This paper is devoted to construct a minimal toric embedded resolution of a rational
singularity via jet schemes. The minimality is reached by extending the concept of the profile
of a simplicial cone given in 6. …