## Arcs and wedges on sandwiched surface singularities.(English)Zbl 0960.14015

Let $$(S,P)$$ be a surface singularity at $$P$$. An arc on $$(S,P)$$ is an algebroid curve going through $$P$$ on $$S$$, given by formal power series in one variable. An arc is general on $$(S,P)$$ if its strict transform on the minimal desingularization is smooth and intersects the exceptional curve $$E$$ transversally at a point lying on a Zariski dense open set of regular points of $$E$$. A wedge on $$(S,P)$$ is a parametrization of $$S$$ by formal power series in two variables; the wedge is centered at an arc if its parametrization comes from the wedge parametrization by simple substitution of two one-variable series. Generally speaking the authors show that a wedge centered at a general arc on a normal surface singularity $$(S,P)$$ lift to its minimal desingularization provided $$(S,P)$$ is a sandwiched singularity, i.e. it is the formal neighborhood of $$P$$ on $$S$$ obtained by blowing up a complete ideal $$I$$ in the local ring of a closed point $$O$$ on a non-singular algebraic surface $${\mathcal X}_0$$ defined over an algebraically closed field $$k$$.

### MSC:

 14J17 Singularities of surfaces or higher-dimensional varieties 13F25 Formal power series rings 14M05 Varieties defined by ring conditions (factorial, Cohen-Macaulay, seminormal) 14B05 Singularities in algebraic geometry
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