On the problem of resolution of singularities in positive characteristic (Or: A proof we are still waiting for)
By Herwig Hauser. 2009
52 citations recorded by the source corpus.
Assume that, in the near future, someone can prove resolution of singularities in arbitrary characteristic and dimension. Then one may want to know why the case of positive characteristic is so much harder than the classical characteristic zero case. Our intention here is to provide this piece of information for people who are not necessarily working in the field. A singularity of an algebraic variety in positive characteristic is called wild if the resolution invariant from characteristic zero, defined suitably without reference to hypersurfaces of maximal contact, increases under blowup when passing to the transformed singularity at a selected point of the exceptional divisor (a so called kangaroo point). This phenomenon represents one of the main obstructions for the still unsolved problem of resolution in positive characteristic. In the present article, we will try to understand it.
Subfields: Algebra and Number Theory, Computational Theory and Mathematics, Geometry and Topology
View Paper: https://www.semanticscholar.org/paper/addead4a33f547416b235cebc9467c598b1f9df7
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In Algebra and Number Theory
In Computational Theory and Mathematics
In Geometry and Topology
Citations in the corpus
- Singularities in positive characteristic, stratification and simplification of the singular locus (2008, background): “e. For instance, the definition of a resolution invariant which works in characteristic zero, but over positive characteristic increases after a finite number of blow-ups at closed points (cf. [18] and [19] for full details). Elimination: a strategy for overcoming the failure of maximal contact in pos”