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

1999/01/11 by Tohsuke Urabe, Urabe, Tohsuke · 2 citations
Mathematics · Computer Science · #Algebraic Geometry and Number Theory #Polynomial and algebraic computation #Commutative Algebra and Its Applications

paper · pdf · doi:10.48550/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.

Cited by

• Newton-Okounkov bodies sprouting on the valuative tree
• Hypersurface Singularities which cannot be resolved in Characteristic Positive

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