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Oberseminar SoSe 2012 Zusammenfassung des Vortrags von Xenia Bogomolec

Lipman's Desingularization Algorithm

If we have a singular 2-dimensional excellent reduced Noetherian scheme, we can use Lipman's algorithm to get a strong desingularization of it. By alternating blow ups and normalizations we finally get a regular scheme. One of the interesting applications are arithmetic surfaces over a Dedekind scheme. The computation of the singular locus in this case is one of the essential things in the algorithm. After outlining some of the important theoretical aspects I will demonstrate the implementation in Singular.