Resolution of Singularities of Germs in Characteristic Positive Associated with Valuation Rings of Iterated Divisor Type
arXiv:math/9901048
Abstract
In this paper we show that any hypersurface singularities of germs of varieties in positive characteristic can be resolved by iterated monoidal transformations in centers in smooth subvarieties, if we have a valuation ring of iterated divisor type associated with the germ. Besides, we introduce fundamental concepts for the study of resolution of singularities of germs such as space germs, iterated analytic monoidal transformations with a normal crossing, Weierstrass representations, reduction sequences, and so forth.
77 pages, AMS-LaTeX 1.2 file. In the third version it is stressed that the article contains not only a result in a special case but also a lot of keys to general cases. This paper has been withdrawn by the author