Singularities in positive characteristic, stratification and simplification of the singular locus

Abstract

We introduce an upper semi-continuous function that stratifies the highest multiplicity locus of a hypersurface in arbitrary characteristic (over a perfect field). The blow-up along the maximum stratum defined by this function leads to a form of simplification of the singularities, also known as a reduction to the monomial case.

Several typos corrected. Minor improvements on the presentation of the published paper

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• Blowups and Resolution
• Desingularization of binomial varieties in arbitrary characteristic. Part I. A new resolution function and their properties
• Nash multiplicity sequences and Hironaka's order function
• Nash multiplicities and resolution invariants
• Finite Generation of Extensions of Associated Graded Rings Along a Valuation
• Nash multiplicities and isolated points of maximum multiplicity
• The asymptotic Samuel function and invariants of singularities
• Contact loci and Hironaka's order
• Finite morphisms and Nash multiplicity sequences