On the classification of rational surface singularities

Journal of Singularities
volume 7 (2013), 108-133

Received: 28 March 2012.

DOI: 10.5427/jsing.2013.7g

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Abstract:

A general strategy is given for the classification of graphs of rational surface singularities. For each maximal rational double point configuration we investigate the possible multiplicities in the fundamental cycle. We classify completely certain types of graphs. This allows to extend the classification of rational singularities to multiplicity 8. We also discuss the complexity of rational resolution graphs.

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