On sandwiched singularities [Elektronische Ressource] / vorgelegt von Konrad Möhring

On Sandwiched SingularitiesDissertation zur Erlangung des Grades\Doktor der Naturwissenschaften"am Fachbereich Mathematik derJohannes Gutenberg-Universitat in MainzVorgelegt vonKonrad Mohring aus Berlinam 26. November 2003D77 Mainzer DissertationTag der mundlic hen Prufung: 20. Februar 2004Introduction2A sandwiched singularity is a surface singularity on the blowup of C in anideal de ned by in nitely near points. Sandwiched singularities have beenstudied by many authors including Zariski [Zar39], Lipman [Lip69], Hironaka[Hir83], and Spivakovsky [Spi90]. The deformation theory of sandwichedsingularities has been studied by de Jong and van Straten in [dJvS98].Sandwiched singularities are rational, in particular they are normal. Ingeneral, they are not complete intersections and there are no particularlysimple or nice equations for them. For example, cyclic quotient singularitiesare sandwiched, and more generally, all rational singularities with reducedfundamental cycle (sometimes called minimal surface singularities) are sand-wiched. Hence sandwiched singularities constitute a large class of rationalsingularities, and we cannot expect to get easy access to information aboutthem by looking at their equations.