Resolution of Singularities of Germs in Characteristic Positive Associated with Valuation Rings of Iterated Divisor Type

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.