2009/10/28 by H. Hauser · 1 citation
Mathematics · Computer Science · #Algebraic Geometry and Number Theory #Polynomial and algebraic computation #Commutative Algebra and Its Applications #Resolution of singularities #Gravitational singularity #Singularity #Mathematics #Dimension (graph theory) #Variety (cybernetics) #Algebraic variety #Resolution (logic) #Zero (linguistics) #Field (mathematics) #Algebraic number #Pure mathematics #Mathematical analysis #Computer science #Artificial intelligence #Statistics
paper · pdf · doi:10.1090/s0273-0979-09-01274-9
openalex publication_date 2009/10/28 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/07
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 <italic>wild</italic> 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 <italic>kangaroo point</italic> ). 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.