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

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

2008-07-27

arxiv.org/abs/0807.4308v3

Adv. in Math. 224 (2010)1349-1418

Mathematics

Algebraic Geometry

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

Scientific paper

10.1016/j.aim.2010.01.005

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.

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