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

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

1999-01-11

arxiv.org/abs/math/9901048v4

Mathematics

Algebraic Geometry

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 cas

Scientific paper

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.

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